close

Вход

Log in using OpenID

embedDownload
UK UNLIMITED
ATOMIC WEAPONS RESEARCH ESTABLISHMENT
AWRE REPORT NO. 024183
The Mk IIIC Vertical Component Force-Balance Seismometer System.
Part 1: Design and Development
R F Burch
Recommended for issue by
A Douglas, Acting Superintendent
Approved by
F E Whiteway, Head of Division
1
UK UNLIMITED
ISBN 0 85'518153 2
CONTENTS
Page
SUMMARY
.
1.
INTRODUCTION
1.1
1.2
1.3
History of t h e development of t h e Mk IIIC seismometer
UKNET
BNA :
'
CONVENTIONAL AND FEEDBACK SEISMOMETERS
Theory of force-balance feedback seisrnometers
Stability of t h e feedback loop
Calibration of seismorneter systems
THE SIGNAL CIRCUITS O F THE MK IIIC FEEDBACK
SEISMOMETER SYSTEM
3.1
3.2
3.3
Transfer function of t h e f o r c e feedback loop
Transfer function of t h e closed loop system (ACC output)
Transfer function of t h e signal circuits following t h e
main feedback loop
4.
DYNAMIC RANGE O F THE SEISMOMETER AND
RECORDING SYSTEM
4.1
System noise
Dynamic range of t h e VBB system
Dynamic range of t h e LPNB system
The optimum broad band response
4.2
4.3
4.4
5.
COMPARISON BETWEEN RECORDINGS FROM UKNET
USINC THE MK IIIC SYSTEM AND THOSE FROM BNA
USINC CONVENTIONAL SEISMOMETERS
5. l
5.2
Signals from an underground explosion
Spectra of seismic noise
6.
CONCLUSIONS
REFERENCES
4
~
CONTENTS (conttd)
Page
APPENDIX A: THE TRANSFER FUNCTION OF THE
CAPACITANCE TRANSDUCER AND
PREAMPLIFIER
52
APPENDIX B: BROWNIAN MOTION AND SEISMOMETERS
55
P
?
APPENDIX C: THE NOISE EQUIVALENT ACCELERATION
OF THE TRANSDUCER NOISE AND
BROW NIAN NOISE
-
FIGURES ,l 39
59
60
SUMMARY
AWRE, Blacknest have developed, in co-operation with t h e University
of Reading, a broad band seismometer system for t h e measurement of t h e
vertical component of ground motion. The system is now deployed at a network
of recording sites throughout t h e UK. The seismometer is a Willmore Mk IIIA
t h a t has been modified in various ways, t h e most important of which is t h e
a t t a c h m e n t of a capacitative transducer t o measure t h e relative displacement of
mass and frame; t h e modified seismometer is thus referred t o as t h e Mk IIIC (C
for capacitor).
Although t h e Mk IIIC uses t h e inertial mass and suspension of a
conventional short period seismometer, t h e inclusion of a displacement transducer and a feedback technique known as "force balancew enables t h e instrument
t o provide adequate signals over t h e frequency band of seismological interest
from 0.01 t o 10 Hz and eliminates t h e requirement for a separate long period
seismometer.
This report is in t w o parts. P a r t 1 (this report) t r a c e s t h e history of
t h e development of t h e system, discusses t h e shortcomings of conventional
instruments and presents t h e theory and transfer functions of t h e feedback and
subsequent signal circuits. The methods of routine calibration of conventional
seismographs a r e discussed and a r e found t o be inadequate f o r use with feedback
instruments. C o r r e c t calibration requires monitoring of t h e instrument output
with t h e feedback loop disconnected.
No currently available digital recorder c a n accommodate t h e large
dynamic range of t h e basic feedback seismometer. A fifteen bit digital recording
system is used here; this limits t h e dynamic range t o a nominal 86 db. The
seismometer output is amplified and filtered so as t o make best use of t h e range
of t h e recorder. A more realistic e s t i m a t e of t h e dynamic range is obtained using
model spectra for teleseismic earthquake and explosion signals and is expressed
in t e r m s of body wave magnitude mb. The surface wave magnitudes MS a r e
calculated using single frequency amplitude values. Typical values of dynamic
range a r e f o r mb from 3.3 t o 7.1 and for M, from 2.1 t o 6.4 (assuming a
recording distance (A) of 72'). These ranges a r e recalculated in t h e presence of
different samples of seismic noise from which i t is seen t h a t t h e range decreases
t o zero when, under t h e noisiest condition, t h e spectrum of a n event of
a
magnitude mb = 6.8 only just exceeds t h e noise spectrum at all frequencies but
at t h e s a m e t i m e t h e sum of t h e t w o spectra causes t h e system t o overload.
A brief analysis is made of teleseismic recordings from an underground explosion. A comparison is made of t h e signal amplitudes and waveshapes
f o r both SP body waves a n d surface waves derived f r o m broad band recordings
from four feedback systems located at s i t e s across England a n d Wales a n d from
four sites (that use conventional long period seismometers) local to Blacknest.
There is close agreement in wave shapes and magnitudes, t h e difference in
magnitudes being only 0.1 to 0.2 units, which is remarkably small.
P a r t 2 (AWRE Report 025183) is a technical description of t h e
seismometer and i t s associated electronic circuits a n d includes detailed
instructions f o r assembly and calibration.
1.
INTRODUCTION
The. first seismographs were insensitive mechanical devices t h a t
recorded ground displacement over a range of frequencies from about 0.1 to a
f e w Hertz. These devices usually contained (like all t h e widely used seismographs
t h a t have been produced subsequently) a relatively large mass a t t a c h e d to t h e
instrument f r a m e by only a spring or a pivot. Ground motion produced a relative
displacement between t h e mass and f r a m e which was mechanically magnified and
recorded as a visual seismogram. Now, in addition to t h e ground motion caused
by seismic disturbances (earthquakes and explosions), t h e surface of t h e e a r t h is
in constant motion due t o seismic noise which is generated mainly by t h e e f f e c t s
of t h e weather and t h e activities of man. The main component of t h e noise is
from oceanic microseisms generated by wind action on t h e sea surface; t h e s e
microseisms have frequencies in t h e range from about 0.12 t o about 0.17 Hz and
reach peak amplitudes of about 20 pm. The oceanic microseisms if recorded
unattenuated tend t o swamp all but t h e largest signals from earthquakes. As t h e
first seismographs produced visual seismograms only and t h e r e was no possibility
of applying any filtering t o improve signal-to-noise ratios, t h e magnification was
usually set s o t h a t t h e noise was just visible on t h e record. In practice, t h e
mechanical seismographs did not have t h e potential to o p e r a t e at much higher
magnifications anyway.
,
With t h e introduction of t h e rnagnetlcoil transducer to convert
relative motion of mass and f r a m e to electrical signals (a mass-frame system
with a transducer t h a t produces electrical signals usually being referred t o as a
seismometer) t h e way was open for t h e use of seismometer-galvanometer
combinations to increase t h e sensitivity of seismographs and to allow frequency
filtering t o be applied to attenuate t h e main noise peaks. Most seismographs in
current use a r e seismometer-galvanometer combinations and a r e of two main
types: short period (SP) seismographs which record ground motion at frequencies
of about 1 Hz (1 s period), t h a t is frequencies greater than those of t h e oceanic
microseisms, and long period (LP) seismographs which record ground motions
with frequencies of about 0.05 Hz (20 s period), t h a t is frequencies below those
of t h e oceanic microseisms. in t h e SP band, compressional or P (Primary) waves
from distances of > 3000 km a r e recorded with maximum signal-to-noise ratio; i t
is from t h e arrival times of these signals t h a t t h e epicentres of most seismic
disturbances a r e estimated. The main signals recorded by LP seismographs a r e
surface waves which, as their name suggests, a r e waves t h a t propagate along t h e
surface of t h e earth and which diminish with depth below the earth's surface; P
waves on t h e other hand a r e body waves t h a t pass through t h e earth.
By t h e 1950's seismometers were available t h a t were adequate for
most seismological needs (l). However, in 1958 a conference held in Geneva
(called t h e Conference of Experts) t o look at ways of monitoring compliance with
any t r e a t y t h a t might b e signed to ban nuclear tests, concluded t h a t t h e only way
of detecting nuclear explosions fired underground was by t h e seismic signals they
would generate; this led t o intensive research on methods of detecting and
identifying underground explosions by seismic means and included studies on ways
of improving conventional seismographs. As a result of this work several new
types of seismometer of high reliability and sensitivity were produced and by t h e
middle of t h e 1960's well engineered L P and SP seismometers t h a t were capable
of recording down to t h e seismic-noise level over all t h e frequency range of
interest, say, 0.01 t o 10 Hz, were commercially available.
In 1959 responsibility for research in t h e UK on forensic seismology
(that is on methods of detecting and identifying underground explosions) was
given t o AWRE*. Some work was done at AWRE on seismometer design in t h e
(2,3) but when seismometers of suitable
early years of t h e research
design became available commercially this first phase of seismometer research
at AW RE ceased.
The past 20 years have seen not only improvements in seismometers
but also improvements in the methods of recording seismic d a t a particularly with
t h e introduction of magnetic t a p e recording. Initially magnetic tape recorders
were used simply t o record more or less t h e same data t h a t was written on to
conventional SP and L P visual seismograms. However, a better way t o record
d a t a when a magnetic tape recorder is used is t o record as wide a band of
frequencies as possible and filter these data on playback as required, t o obtain
seismograms with optimum signal-to-noise ratio. Over t h e past 10 years a
number of research groups, including t h a t at Blacknest, have demonstrated that
there a r e advantages in recording wide band (say, 0.01 to 5 Hz) seismic data with
t h e whole bandwidth covered by one type o i seismometer.
The simplest way t o achieve wide band recording using electronic
amplification is t o use an LP seismometer. Such instruments a r e bulky and heavy
(- 80 kg) and sensitive t o changes in temperature and pressure but environmental
e f f e c t s can be minimised by careful design, precision engineering and t h e
provision of a large but rigid pressure-jacket with good thermal insulation. The
research group at Blacknest has been operating such a broad band (BB) recording
system since 1970 using high quality LP seismometers of conventional design
(Geotech S-11%) and electronic amplification. Such has been t h e improvement in
t h e design of LP seismometers since 1958 that, whereas early designs needed
daily attention, two Geotech S-11's operated by Blacknest at two different sites
have required no attention whatsoever for t h e past 8 years. (Some recordings
from these instruments a r e shown in section 5.) ~ l t h o u g ht h e inertial mass in
these instruments has drifted within t h e working range during operation, they
have continued to operate satisfactorily because t h e magnetlcoil transducers
give an output t h a t depends on t h e relative velocity of mass and f r a m e (they a r e
*In 1959 AWRE was part of t h e United Kingdom Atomic Energy Authority. In
1973 AWRE was transferred t o t h e Ministry of Defence. Over t h e whole of t h e
t i m e AWRE has been responsible for UK research in forensic seismology and
since 1961 t h e bulk of t h e research has been carried out a t Blacknest, an
outstation of AWRE.
velocity transducers as opposed t o displacement transducers which give an output
proportional t o t h e relative displacement of mass and frame) and w a r e not
sensitive t o long-term drift.
It has been demonstrated t h a t t h e BB recording system described
above can be used t o simulate both SP and LP seismograms and use of this type
of system has been advocated by t h e Blacknest group (4) as a way of getting SP,
LP and BB seismograms without t h e need for separate S P and LP seismometers.
Since November 1975 a n array of four Geotech S-l1 seismometers has been in
operation at Blacknest producing broad band recordings. The response of these
recording systems differs somewhat from t h a t of t h e original BB system for,
whereas the original system had a frequency response t h a t was constant for
constant amplitude of ground displacement in t h e pass band, t h e latest system
has a response that is constant for constant amplitude of ground velocity in t h e
pass band. As the response of a seismometer equipped with a velocity transducer
is flat t o ground velocity at all frequencies above t h e natural frequency, by
simply applying a low noise amplifier t o the output of a Geotech S-l l (natural
frequency 0.05 Hz) gives a response that is flat t o ground velocity over t h e major
portion of the pass band of interest; this response t h a t is flat to velocity is
termed the Velocity Broad Band (VBB) response. The principle disadvantage of
VBB systems built around conventional LP seismometers is t h a t t h e seismometers
a r e expensive and, being large, difficult t o handle.
In t h e l a t e 1960's it was suggested that L P seismometers could be
made much smaller than those in current use by designing them to operate with
electronic feedback and this stimulated new research programmes t o design
compact instruments t h a t would allow both SP and LP recordings t o be made
from the same seismometer. Such miniature seismometers t h a t would record all
frequencies of interest would be much easier to isolate from environmental
changes than large instruments; they could also be easily installed in boreholes.
Installing seismometers in boreholes has two advantages:(a) The borehole reduces the effect on the seismorneter of surface
variations in tcmperatureand pressure, and
(b) Seismic noise tends to decay with depth so that signals recorded
from borehole seismometers should have larger signal-to-noise ratios
than those recorded from surface instruments.
Various seismometers that would operate in boreholes and produce LP recordings
were designed using conventional principles but none, of these seem to have been
entirely satisfactory.
More recently t h e Blacknest research group began a co-operative
project with t h e Department of Cybernetics at t h e University of Reading to
develop feedback seismometers and investigate t h e possible advantages of their
use in wide band recording. The specific objective of this project was to develop
a feedback seismometer t h a t could be installed in a shallow 8 in. diameter
borehole.
Two types of feedback seismometer were developed during t h e cooperative project. One system is based on a small commercially available SP
seismometer (a Willmore Mk IIIA) which has been modified t o operate as a
feedback instrument; this instrument is known as t h e Mk IIIC. The second type of
instrument is a borehole system built around mechanical systems developed by
t h e University of Reading.
This report describes the design and development of t h e Mk IIIC
system. The system has been thoroughly tested and is currently being installed at
a network of sites in t h e UK (UKNET; see section 1.2). Examples of signals
recorded by t h e Mk IIIC systems of UKNET a r e presented and t h e signals a r e
compared with signals recorded by Geotech S-l1 seismometers of t h e Blacknest
array (BNA).
The report also discusses:(a) Some general problems of seismometer design and t h e
advantages and disadvantages of seismometers that use feedback
compared t o those that do not.
(b) The optimum system for recording seismic data t o make best
use of t h e dynamic range of magnetic t a p e (particularly digital)
recording systems.
The report also contains a detailed technical description of the
Mk IIIC system (see Part 2, AWRE Report 025183).
The borehole system which was built a s part of t h e BlacknestUniversity of Reading project is currently undergoing further development and
testing, and will be described elsewhere when development is complete. A brief
history of the co-operative project is given below.
1.1
History of t h e development of t h e Mk IIIC seismometer
In 1966 Professor P B Fellgett of t h e University of Reading showed
( 5 ) t h a t theoretically a seismometer could be designed with a performance equal
t o t h a t of a conventional L P instrument but which used only a small suspended
mass with a displacement transducer and feedback over t h e whole seismic band.
(A number of seismometers and closely related instruments using feedback have
been described in t h e literature (6-10) before 1966 but none of t h e instruments
described was specifically for a seismometer using feedback over t h e whole of
t h e frequency band of interest.) The practical realization of such a n instrument
was delayed mainly because t h e electronic amplifiers t h e n available had
electronic noise levels and drift r a t e s which w e r e t o o high. Stimulated by t h e
publication in 1970 of t h e results obtained by Block and Moore (1l), using a small
q u a r t z seismometer, Fellgett obtained a grant from t h e Natural Environmental
Research Council in 1971 to develop a practical instrument. The project w a s
assigned t o I W Buckner under t h e guidance of M J Usher.
The financing of this project was taken over by AWRE in June 1974
by means of a n Extra Mural Research Contract with t h e Department of Cybernetics, University of Reading and t h e c o n t r a c t continued until 1980, By June
1974 a small horizontal component feedback instrument had been constructed
and tested. Further testing was then carried o u t during 1975 by installing t h e
seismometer in t h e AWRE vault at Wolverton (see figure l ) and directly
comparing t h e outputs with those of t h e Geotech S-11 seismometer system. The
comparison showed t h a t t h e performance of t h e feedback instrument was
satisfactory (12,131.
However, t h e main requirement for AWRE was for a seismometer
measuring t h e vertical component of t h e ground motion, Between 1971 and 1974
t h e University of Reading had designed and made several types of miniature
vertical component mass/spring systems but none proved to be satisfactory. As
t h e feedback principle had been proved with t h e horizontal instrument, t h e
author suggested t h a t our requirement for a vertical. seismometer could most
quickly and simply be m e t by modifying a Willmore Mk II'IA a conventional SP
seismometer even though i t has a large inertial mass of 1.3 kg (compared with
t h e 40 g mass of t h e proved horizontal instrument).
-
-
Theoretical studies showed that t h e feedback system developed by
the University of Reading should be capable of operating with a Willmore Mk IIIA
and work began in 1975 on developing such a feedback seismometer; this work led
t o the development of t h e Mk IIIC. The prototype of t h e Mk IIIC was produced by
Usher and Guralp of t h e University of Reading and ancillary circuits were
designed at Blacknest t o enable t h e instrument to operate with t h e standard
Blacknest recording system. Usher, Burch and Guralp (14) described a laboratory
version of t h e Mk IIIC that operates on mains power.
Further development and redesign has been undertaken to enable t h e
complete system t o operate unattended a s a component of a network o r a n
element of an array. Such a network is UKNET.
1.2
UKNET
The Mk IIIC system is designed t o be powered from either mains or
batteries and t o transmit the output signals in FM form over either cables or
British Telecom telephone lines t o a recorder. The system has been tested in
various modes of operation and several instruments a r e now in continuous
operation. The most extensive use of t h e system has been in UKNET.
UKNET is a network of 9 stations (figure l and table 1) in t h e UK,
eight of which a r e equipped with a Mk IIIC system and with the output signals
transmitted over British Telecom lines t o recorders at Blacknest. Five of t h e
Mk IIIC systems a r e installed in Royal Observer Corps (ROC) posts and t h e
equipment is powered by batteries; three stations of UKNET a r e at existing
seismological stations and have mains power. The first three stations of UKNET
were installed in the summer of 1981 and installation of the full network was
completed by early 1983. The one non-standard station is that at an ROC post in
Cornwall (SBD). The instrument is a conventional SP seismometer and is due for
conversion t o the Mk IIIC system in July 1983.
Two multiplexed f requency-modulated (FM) signals can be transmitted
from each station. In routine operation these a r e a broad-band output which has a
response a s a function of frequency that is constant in t h e passband (0.02 t o
4 Hz) t o an input which has a flat amplitude spectrum for ground velocity (the
response is very similar t o the VBB response of the BNA) and an LP narrow band
(LPNB) output which has a response that is sharply peaked at about 0.04 Hz. The
LPNB signal could be derived from t h e VBB signal after- transmission but, as two
channels a r e available from each station t o Blacknest and t h e LPNB is easily
formed at t h e station, i t is convenient t o transmit both VBB and LPNB signals.
At Blacknest t h e VBB signals a r e fed into 'a special purpose device t o
convert t h e FM signal direct t o digital form without t h e need for demodulation
(15). The LPNB signals however a r e first demodulated and t h e resulting analogue
signals a r e then converted t o digital form using a conventional ADC device. The
VBB signals a r e written on to t a p e at 10 samples/s (giving a Nyquist frequency of
5 Hz)and t h e LPNB at l sample/s (giving a Nyquist frequency of 0.5 Hz).
BNA
-
1.3
The Mk IIIC system is now being used t o increase t h e number of
elements in this local a r r a y t o 10. Additional sites a r e already in existence, and
connected with mains power and telephone lines. Four sites in this a r r a y (figure 1
and table 1) have been in continuous operation since 1974 using Ceotech S-l l
long period seismometers t o generate t h e VBB response. Two emplacements
(BKN and WOL) a r e seismic vaults whereas t h e instruments at HD and BW a r e
installed in large fibreglass containers with t h e seismometer 6 f t below ground
surface. For t h e additional future installations t h e Mk IIIC instruments will be
installed in I m length of 8 in. diameter steel pipe t h e top of which will b e just
below t h e ground surface.
TABLE 1
Co-ordinates of Broad Band Recording S i t e s
(a)
UKNET
EKA
MMY
CWF
LLW
LAM
SCK
BHM
WOL
Eskdalemuir, S c o t l a n d
Middlesmoor, Yorkshire
Charnwood F o r e s t , L e i c e s t e r
Llanuwychllyn, Wales
Lampeter, Wales
South Creek, Norfolk
Barham, k e n t
Wolverton, Hampshire
lackne nest Local Array)
(b)
HD
Headley
BW
WOL
Bucklebury West
Wolverton
BKN
Blacknes t
CONVENTIONAL AND FEEDBACK SEISMOMETERS
The design of a conventional seismometer depends on t h e component
of ground motion t o b e measured. T o measure vertical motion t h e mechanical
system is usually a mass suspended by a spring; t o measure horizontal motion
some form of pendulum is usually used. For simplicity conventional seismometers
a r e discussed below in t e r m s of vertical-component instruments but most of t h e
discussion also applies t o horizontal-component seismometers.
A mass-spring system has a natural frequency of oscillation
bo)and
once disturbed will, in t h e absence of any damping, oscillate for ever; such a n
instrument is of l i t t l e use. Damping has therefore t o b e applied t o turn t h e massspring system into a practical instrument for measuring ground motion; in a
seismometer such damping is usually electrical. For ground disturbances with
frequencies W well above W t h e mass effectively does not move s o t h a t t h e
relative motion of mass and f r a m e is a direct measure of ground displacement.
At frequencies well below W t h e relative motion of mass and f r a m e decreases
a s (w/w0)' decreases and at very-low frequencies t h e mass effectively follows
t h e frame.
If t h e relative displacement of mass and f r a m e at frequency W is
written a sin wt, then their relative velocity is a cos o t and so t h e output for a
velocity transducer falls off with decreasing frequency for constant amplitude of
relative displacement. Thus, at frequencies well below w t h e response t o
constant amplitude of ground displacement for a seismometer with a velocity
This r a t e of fall-off c a n b e used to
transducer is proportional t o (w/w,)'.
advantage in a n SP seismometer designed t o d e t e c t signals of about 1 Hz and
a t t e n u a t e oceanic microseisms because by settingw ,/2n
= l Hz, then
micro-
seism signals with frequencies of, say, 0.15 Hz will b e reduced in amplitude
relative t o signals at l Hz by a f a c t o r of about ( 0 . 1 5 ~ ' 300.
Seismometers with velocity transducers w e r e originally designed t o
drive galvanometers for use with a photographic recording system (and many
such instruments a r e still in operation) without a n y means of electronic
amplification. The natural frequency of t h e galvanometer is also chosen to reject
frequencies of ground motion where the signal-to-noise r a t i o is low. Thus, a 4 Hz
galvanometer is often used with SP systems t o reject high frequency man-made
(sometimes called cultural) noise d u e t o railways, t r a f f i c on roads, factories a n d
s o on. With LP seismometers, galvanometers a r e used with natural frequencies of
about 0.01 1 Hz (90 S period) to give a **bassboost1* e f f e c t and again a t t e n u a t e
ground motion at t h e frequencies of t h e seismic microseisms. Conventional LP
and SP seismographs of t h e above t y p e allow signals t o b e recorded in pass bands
on either side of t h e oceanic microseism peak, t h a t is in bands where t h e signalto-noise ratio will usually be greatest. Examples of typical SP and LP responses
a r e shown in figure 2. Note t h a t in practice such LP systems d o not a t t e n u a t e
oceanic microseisms very effectively.
The introduction of electronic amplification enables electronic filters
t o be used t o a t t e n u a t e oceanic microseisms and it might appear t h a t i t would b e
possible t o t a k e any seismometer and simply apply filters t o shape any required
system response. However, it is difficult t o obtain satisfactory recording of LP
ground motion using a conventional seismometer other than one with W 0 near or
below t h e frequencies of t h e ground motion of interest. As noted above t h e
output of a seismometer with a velocity transducer falls off as U' below W s o
if wo lies well above t h e frequencies of interest, t h e output of t h e seismometer
will be low. Now in t h e LP pass-band, t h a t is at frequencies of 0.05 Hz (20 s
period) and smaller, electronic noise is proportional t o U-' (this is t h e so-called
l/f noise) so t h a t in trying t o use a seismometer with w well above t h e
frequencies covered by t h e LP pass-band, not only is t h e output signal weak but
electronic noise of conventional amplifiers tends t o b e large; to design a n
amplifier with electronic noise low enough t o allow weak signals to be seen above
t h e noise is difficult.
The effects of electronic noise can b e reduced if a capacitance
displacement transducer is used. For although at signal frequencies of a few
Hertz both displacement and velocity transducers have t h e same signal-to-noise
ratios, t h e ratio decreases for velocity transducers as t h e frequency of t h e signal
decreases whereas for displacement transducers i t remains constant. Capacita n c e transducers also have t h e advantage t h a t they can b e made small and light,
whereas t o obtain a high signal-to-system-noise ratio from a velocity transducer
i t must b e physically large (a strong magnet and a coil of many turns).
It can b e shown t h a t a small S P seismometer (with o o / 2 n = 1 Hz)
with a displacement transducer c a n be made t o have a performance at long
periods equivalent t o t h a t of a large and more expensive conventional LP
seismometer (with w o/2 n = 0.05 Hz) t h a t has a velocity transducer. Thus, i t
would appear t h a t by fitting a displacement transducer to an SP seismometer t h e
required broad band seismometer could be produced. However, t h e r e a r e two
disadvantages with such a system: (a) there is a corner in t h e response at
,l2 n = I Hz due t o t h e natural frequency of t h e mechanical system and as
this corner lies in t h e seismic band of interest it may be undesirable, and (b) a
displacement transducer gives an output proportional t o t h e slow drift of t h e
mass from its initial position due t o environmental changes and this results in
large offsets on t h e signal-output voltage and in non-linearity.
It might b e argued that at least t h e difficulty with t h e corner in t h e
response could be overcome by making t h e natural frequency of t h e seismometer
much greater than 1 Hz. Such a mass-spring system would be easy to construct
but as the output is inversely proportional to W
below t h e natural frequency,
this would again result in poor signal-to-electronic-noise ratios.
Both the problem of t h e corner in the response in t h e pass band of
interest and t h e problem of drift can be overcome by t h e use of electronic
feedback. The feedback takes t h e form of a force t h a t is applied t o t h e inertial
mass by a simple magnetfcoil transducer which can be of low efficiency as t h e
only requirement is t h a t it produces a force proportional t o t h e current through
t h e coil. The force is arranged t o be proportional t o t h e relative displacement of
mass and f r a m e produced by t h e ground motion. 'The e f f e c t of t h e feedback is t o
a t t e m p t t o oppose relative p o t i o n of t h e mass and f r a m e which effectively
stiffens t h e suspension and so increases t h e natural frequency of t h e seismometer. Provided t h a t no e x t r a noise is introduced into a system, t h e use of
feedback does not change t h e signal-to-electronic-noise ratio so t h a t in this way
t h e acceptable signal-to-noise ratio of a 1 Hz seismometer is retained but with
t h e added advantage t h a t t h e corner in t h e response is now o u t of t h e signal
band. In addition, drift of t h e mass is reduced as t h e sensitivity of t h e
seismometer to environmental changes is proportional to (l/@ o)
'.
The use of feedback has other advantages as well as those given
above; for example, t h e linearity of a seismometer using feedback is much better
than t h e equivalent seismometer without feedback. Also because both t h e natural
frequency and sensitivity of a feedback instrument depend principally on t h e
feedback parameters, then t h e spring of t h e suspension system and t h e
capacitance plates of t h e transducer do not have to b e made with small
tolerances and this simplifies manufacture.
The reduction in size t h a t is possible with feedback seismometers is
only limited in theory t o t h e dimensions at which t h e Brownian noise of t h e
suspended mass approaches t h a t of t h e electronic noise of t h e transducer. This
suggests t h a t masses of t h e order of a few grams could be used (instead of
kilograms for conventional instruments), although in practice i t is necessary t o
increase t h e dimensions t o t h e order of
and reliable suspension systems.
100 g in order t o manufacture simple
2.1
Theory of force-balance feedback seismometers
2.1.1
Response t o give a constant output t o ground acceleration
To develop t h e theory of feedback seismometers we consider first t h e
(open loop) response of a mass-spring system. The relationship between xr t h e
displacement of t h e mass relative t o t h e frame and 2 is given by
X
= (S' + 2nou0f +
U:)-'
,
where W is t h e natural frequency of t h e system, no is t h e damping factor and s
is the Laplace operator U + jw. If a displacement transducer-amplifier combination with a sensitivity of A V/m is used t o measure t h e relative motion of mass
and frame, t h e output sensitivity is
where v. is t h e output voltage. The frequency response of such a system is shown
in figure 3.
Ignoring t h e e f f e c t of damping i t can be seen t h a t t h e response is f l a t
to ground acceleration from 0 t o fo HZ (where fo = wo/2 n) and has a sensitivity
below fo of A/
volts/m/s2 (equation (l)). The response at frequencies above
fo falls off a s w2, t h a t is t h e response is f l a t for constant ground displacement.
For signal frequencies about fo t h e response is dependent on t h e
damping of t h e mass-spring system. For small seismometers this natural
frequency is usually in t h e SP band at about 1 t o 2 Hz. We now look at how f f o r
0
a seismometer can b e increased by using feedback; in this way t h e natural
frequency of a n SP seismometer can be moved t o higher frequencies o u t of t h e
pass band t o give a n output f l a t t o ground acceleration through t h e entire range
of seismic frequencies of interest;
A diagram of t h e force feedback seismometer is shown in figure 4(a).
The amplified output of t h e displacement transducer is connected via a parallel
RC combination t o a force transducer (magnet/coil assembly with a sensitivity of
G Newtons/Ampere) which is also mounted between t h e mass and frame. Such
feedback seismometers a r e usually referred t o as llclosed loopw systems because
part of t h e output is fed back around a loop; this distinguishes this type of
seismometer from those without feedback which can thus b e considered as "open
looptt systems.
A block diagram of t h e system is shown in figure 4(b) showing a
summing junction of t h e forces on t h e inertial mass. A simplified form is
shown in figure 4(c) from which these forces can be equated
MY B V, = Vo/KA which re-arranged gives t h e basic feedback equation of
-
-= M
"0
X
KA
(1 + W) =
as
(forward path)
(1 + complete imp path)*
This gives t h e seismometer voltage output sensitivity for ground motion
acceleration. It is immediately seen t h a t if KA B >> l, then i t reduces t o
Vofi = M/ k , ie, only dependent on t h e feedback fraction
The parameters of figure 4(a) can be used t o derive B as follows:J
The impedance Z of t h e R C combination is R(1 + SCR)-' and this
allows a current i (= Vo/Z) t o pass through t h e feedback coil and generate an
opposing force of Gi Newtons. But B = force/Vo = Gi/Vo = G(l + sCR)/R. Replacing K with (h4(s2 + 2n0uOs + %))-l and B with C(l+sCR)/R in t h e equation for t h e
acceleration sensitivity shown above gives
If A, R and C a r e t h e only variables, then
(a)
If R
+ a and
C + 0, t h e expression reverts to t h e open loop
case,
(b) If AGIMR >> W: , t h e acceleration sensitivity of t h e seismometer at low frequencies 0 Hz)is given by vo/Y = MR/G, t h a t is
t h e sensitivity depends on R only.
(C)
The new natural frequency WO is (W
greater than W o; if AG/MR >>
and R and not w o.
W
',,
+ AG/R)
+ which is
then WO depends mainly on A
(d) The new damping factor No is (2nooo + CAG/M)/W, and for
AGlMR >> W: then No depends on A, C and R*
From this it is seen that t h e order of selection is: calculate R t o give t h e
required sensitivity, A to give WO and finally C t o give No.
Suppose now we wish t o choose t h e parameters of t h e Mk IIIC t o have
'
a sensitivity vo/Y at 0 Hz of 10' Vlmls ;a value of Fo(= Wo/2r) of 16 Hz and a
damping factor No of 0.7.
Assuming AG/MR>>w;,
this requires
R = 1.23 X 10 Q, A = 1.01 X l 0 V / m and C = 11,32 nF, t h e other parameters
being typical values for a Mk IIIC seismometer of fo = 1.67 Hz (W, = 10.49),
"0
= 0.01, G = 160 NIA with M = 1.3 kg. The truevaluesof t h e sensitivity, F. and
',
No, obtained using t h e above values of R, A and C a r e 9.80 X 10' v l m h
16.09 Hz and 0.697 respectively, that is t h e actual values differ from t h e chosen
values by less than 1%.
The e f f e c t s of varying t h e parameters A and R can also be seen using
t h e Bode plot, a s shown in figure S. We set t h e displacement transducer and
amplifier gain at 1.01 X 10 V/m with a mechanical frequency fo of 1.67 Hr. If
t h e circuit was operating "open loop1@,then t h e d c acceleration sensitivity would
b e A/$
= 9.2 X 10' V/m/s falling off as 2 above t h e natural frequency.
This open loop response is shown by t h e line abe. The response t h a t we have
obtained using feedback is shown as t h e line c d e intersecting t h e open loop
response at frequency F. = 16 Hz and sensitivity = 10' V l m h ?
If we keep t h e transducer gain (A) constant and a l t e r t h e feedback
resistor R t o change t h e sensitivity, then t h e corner frequency will be
determined by t h e geometry of t h e open loop response, eg, for a sensitivity of
10' V/m/s we will obtain a corner a t 5 Hz (line fge). In order to recover our
original corner at 16 Hz at this new higher sensitivity we must increase t h e
transducer gain A by a factor of 10 t o give a new open loop response hij and a
resulting closed loop feedback response fkj. However, we a r e not able to increase
this gain A without limit; above a certain value t h e circuit is unstable and
oscillates with t h e feedback applied. Fortunately this problem of stability is
predictable and is discussed in section 2.2.
2.1.2
Response t o give a constant output t o ground velocity
It has been shown by several research groups t h a t t h e optimum
response for recording ground motion in t h e seismic band of interest is one t h a t
is flat t o ground velocity. Such a response makes better use of t h e available
dynamic range of both seismometer and recording systems and produces a
roughly white spectrum of seismic noise in t h e frequency band of interest (see
section 4.4). So far we have used feedback t o shift t h e unwanted response corner
out of t h e band but this leads to a response t h a t is constant for constant ground
acceleration.
A further disadvantage of this response is i t s high sensitivity to local
cultural noise t h a t generates signals t h a t intrude into t h e high frequency end of
t h e band. This sets t h e limit t o the feedback circuit sensitivity which must not b e
allowed t o overload. Conversion from t h e response f l a t t o acceleration to t h a t of
velocity can be achieved by using a filter (integrator) external to t h e loop but
this will not prevent t h e loop from overloading. For t h e Mk IIIC seismometers
used in UKNET t h e conversion t o a velocity response is made within t h e loop.
The method makes use of t h e properties of t h e response of t h e basic seismometer
when t h e damping t e r m is large. Whereas figure 3 is shown as t h e response t o
acceleration i t is now shown as t h e response to velocity in figure 6 but with
no >>I.
For any value of t h e damping factor no t h e output at t h e natural
frequency fo is (2no)'l times t h e value predicted by t h e intersection on a log-log
plot of t h e asymptote t o t h e response at frequencies below fo with t h e asymptote
t o t h e response at frequencies above fo. If no>> l, then t h e response will be very
nearly flat for ground velocity around fo; t h e response is 3 db down at 2nof0 and
0.5n0f0. Similarly f o r a closed loop system t h e velocity response will b e f l a t
around F. with 3 d b points at 2N0Fo and 0.5N0F0.
As shown earlier t h e damping of t h e feedback seismometer is
determined by t h e value of t h e feedback capacitor C. Unfortunately increasing C
t o t h e value required t o give t h e f l a t velocity response causes t h e loop circuit of
this simple design t o become unstable and e x t r a circuit components must be
included t o prevent this instability.
2.2
Stability of t h e feedback loop
The basic block diagram is shown in figure 4(c) from which t h e
relationship of t h e output t o t h e input (transfer function) was determined a s
Vo/S = MKAMI + KAB).
Although t h e feedback signal is assumed to be real and positive, i t
enters t h e negative summing junction of t h e forces t o give negative feedback.
For the seismometer circuit K, A and B a r e all functions of w (the signal
frequency) and have phase responses t h a t vary with it. From t h e simple equation
above i t can be seen t h a t if t h e phase of KAB totals 180' with i t s amplitude
equal t o unity, then V. will becomeinfinite and t h e system will b e unstable. To
estimate t h e stability of a system it is useful to plot t h e loop transfer locus. This
is a polar graph plot of t h e transfer function of t h e complete loop (KAB) but with
t h e feedback disconnected from t h e summing junction. Amplitude is plotted as
radius against phase for signal frequencies from z e r o to infinity (see figure 7
which is also known as a Nyquist plot). The Nyquist criterion of stability
determines absolutely whether t h e system will be stable o r not but this is
difficult t o apply. The practical use of this plot is t o determine t h e margin of
stability. The system must become'unstable if t h e locus passes through t h e point
-l ,jO. The two margins (phase and grain) a r e shown in figure 7' and empirical
'
values t h a t should be allowed t o give satisfactory performance in its response t o
transients a r e t h a t t h e phase margin should exceed 40' and t h e gain margin
should exceed 50%. The problems with stability mentioned in section 2.1.1 c a n
now b e visualised. For t h e acceleration response (section 2.1.1 and figure 5 ) t h e
corner frequency was increased t o WO by increasing t h e loop gain A. The limit is
approached as t h e gain margin goes to zero. For t h e velocity response (section
2.1.2 and figure 6) t h e damping no was increased t o No by increasing t h e
capacitor C. The e f f e c t of this is t o increase t h e phase lag of t h e loop while t h e
amplitude is still greater than unity and so reduce t h e phase margin. Thus, unless
stability can be maintained by merely reducing t h e gain, components t h a t
generate a phase lead must b e added t o t h e circuit t o decrease t h e phase lag. As
will be seen later (section 3) this does a f f e c t t h e overall response (Vo/f) and
results in small perturbations in t h e flatness of t h e response in t h e passband.
2.3
Calibration of seismometer systems
The requirements and methods of calibrating seismographs depends on
t h e response under investigation. For conventional SP systems i t is often
considered sufficient t o determine t h e seismometer output sensitivity and
damping characteristics in the laboratory, assume its response by checking t h e
natural frequency of t h e instrument in t h e field, and t o thereafter calibrate only
t h e electronic amplifiers, usually at only one specified signal frequency. This is
t h e method used at t h e AWRE sponsored SP array stations and is only acceptable
because the recordings a r e used mainly for event detection purposes and for
approximate amplitude measurements which a r e taken from a n impulsive
waveform. This is not so for L P system recordings where not only is t h e
amplitude of t h e dispersed surface waves required over a wide band, but their
analysis requires their detailed phase relationship as modified by t h e recording
system. The problem is made worse by t h e use of, t h e electronic filters with
sharp attenuation characteristics within t h e band t h a t a r e used in t h e LPNB
systems.
The system (complete with inertial mass) can b e calibrated for both
amplitude and phase if a seismometer is equipped with a "calibration coilw.
The calibration coil consists of relatively f e w turns which a r e
normally wound on t h e same former as t h e main data coil output. Thus, t h e coil
is a force transducer generating a force directly on to t h e inertial mass
proportional to any current passing through t h e coil. This constant is known as
t h e motor constant GC for t h e magnet and coil combination and is only dependent
on t h e strength of t h e magnetic flux and t h e number of turns of t h e coil t h a t is in
t h e flux. If a current i Amperes is passed through t h e coil, t h e force developed on
t h e inertial mass M is Gci Newtons and is thus equivalent .to a ground motion
acceleration of Gci/M m/s2
S
.
One method of calibration is to apply a current s t e p to t h e coil and
then, a f t e r say 2 min, remove it. The resulting waveform is shown in figure 8.
Daily calibrations of this kind a r e easy t o automate and allow a simple visual
check t o be made on t h e operation of t h e system. The waveform c a n in principle
b e analysed using Fourier techniques t o obtain t h e amplitude and phase response
of the seismograph. In practice, this method gives poor results due not only to
t h e presence of seismic noise on t h e recording but also t o t h e f a c t t h a t t h e input
signal (the step of acceleration) is predominantly t h a t of a very low frequency
fundamental with decreasing amplitudes for t h e higher frequency signals.
A second method uses sinusoidal input currents as t h e driving force.
A sine wave of constant amplitude and frequency is applied to t h e coil and a f t e r
allowing several cycles of oscillation for t h e transients to decay to z e r o t h e
steady s t a t e amplitude of t h e system output c a n b e measured with i t s phase
relative t o t h e input current. The response can thus b e determined for any signal
frequency in t h e band. In practice, t h e theoretical response of t h e system is
known and this sinusoidal current method is used only to check t h e amplitude
response at a few spot frequencies.
The calibration methods described above a r e routinely used for both
conventional and feedback seismometer systems. Unfortunately this simple
procedure will not d e t e c t any,change in sensitivity for t h e feedback system t h a t
would be recognised with a conventional seismometer system. Consider t h e
simplified signal and calibration circuits for t h e conventional and feedback
instruments shown in figures 9(a) and (b). As stated above t h e value of t h e
calibration coil constant G, is a function only of t h e number of turns in t h e
winding and t h e strength of t h e magnet. Suppose t h e magnet strength is halved,
then t h e sensitivity of t h e conventional system will be halved as will t h e motor
constant Gca of t h e calibration coil. This will result in output calibration signals
with an amplitude of one-quarter of those previously obtained. The sensitivity of
t h e feedback system will have doubled because, as shown in section 2.1, t h e
sensitivity is MR/G. But t h e motor constant of t h e calibration coil Gcb is again
halved and so t h e resulting output calibration signals will have a n identical
amplitude even though t h e sensitivity has doubled.
In some small feedback seismometer systems a common coil is used
for both t h e feedback and for calibration; this does not a l t e r t h e above reasoning
but leads t o t h e single equivalent diagram of figure 9(c). For very low
frequencies, if t h e input calibration current is derived from a generator of V.
m
volts and passed through a resistor of equal value to t h e feedback resistor Rp,
then the output signal voltage will be numerically t h e same value but reversed in
sign. This again demonstrates t h e failure- of this calibration system t o d e t e c t
changes in sensitivity.
Therefore if t h e calibration coil system is to be used with confidence
with feedback systems, t h e force transducer must b e completely independent of
t h e feedback coil with i t s own separate magnet. If this is not possible, then t h e
calibration coil only needs to b e routinely relatively calibrated with t h e feedback
connection disconnected (open loop). For an instrument with,separate coils (such
as t h e Mk IIIC), this open loop method becomes t h e same configuration as t h e
conventional seismometer system (figure 9(a)) where t h e feedback coil is now
used as a signal (data) coil (GD), t h e output from which is amplified and t h e
waveform t h a t results from a current s t e p is observed as in figure 8 but of a n
oscillating nature due to t h e lack of damping.
For an instrument with only one coil t h e output from t h e displacement transducer can be taken and displayed. This signal will consist of a n
oscillating waveform superimposed on a s t e p displacement of t h e recording due
to the displacement of t h e mass. For both types of instrument a direct check on
t h e natural frequency of t h e seismometer suspension and i t s damping is an
additional feature of this method.
3.
THE SIGNAL CIRCUITS O F THE MK IIIC FEEDBACK
SEISMOMETER SYSTEM
The principal components of t h e seismometer signal circuits a r e
shown in figure 10. Full circuit diagrams and component values a r e given in
P a r t 2 (AWRE Report 025/83).
The displacement transducer is a differential capacitor; t h e outer two
capacitor plates (upper and lower) a r e attached to t h e f r a m e of t h e seismometer
and the inner plate is attached to t h e mass. In t h e absence of ground motion t h e
spring supporting t h e mass is adjusted so t h a t t h e inner plate is in a central
position between t h e two outer plates. When an acceleration is applied t o t h e
frame, i t moves and the mass tends t o remain in a fixed position with t h e result
t h a t t h e inner plate is displaced from its central position.
The method used to measure t h e displacement is t o apply a constant
amplitude carrier signal of 50 kHz t o each of t h e outer plates but with opposite
phase. This results in zero voltage output when t h e inner .plate is central.
Displacement of t h e inner plate gives a 50 kHz output signal with its amplitude
proportional t o t h e displacement and with a phase shift relative to t h e drive
oscillator of 0 or n depending on whether t h e central plate moves up or down
respectively.
The output of t h e differential capacitor is now fed via a preamplifier
and two high-frequency amplifiers (together called t h e channel amplifier) t o a
circuit known as a phase sensitive detector t h a t converts t h e 50 kHz output
signal into an analogue voltage t h a t is directly proportional t o the displacement.
The analogue signal is then passed through a "controller" stage whose
purpose is t o ensure stability of t h e feedback loop and optimise i t s performance.
In t h e absence of this stage t h e feedback current and hence t h e force would be
proportional t o t h e analogue voltage signal of t h e mass displacement. The
addition of a capacitance in t h e feedback of t h e controller amplifier integrates
t h e signal at low frequencies and in this form is known as a Proportional plus
Integral (or P + I) controller. The advantages of t h e addition of integral control
a r e two-fold: t h e infinite gain as U + 0 allows a large amount of feedback t o b e
employed with safety as t h e phase margin is 90' (as will b e w e n later), and t h e
response of t h e system t o a disturbance is enhanced, allowing t h e system t o
recover in a minimum time. A further addition t o this controller is a phase lead
circuit consisting of a resistor and capacitor in parallel. The purpose of this
arrangement is t o maintain stability of t h e loop.
The output of t h e P + I stage, which is referred to as t h e acceleration
(ACC) output of t h e system, is now fed back via a resistor and capacitor in
parallel t o one of t h e main velocity transducer coils of t h e original Mk IIIA
seismometer.
Provided t h a t t h e gain in t h e feedback loop is high, t h e ACC output
is flat t o ground acceleration from z e r o frequency t o 0.05 Hz (20 S period); from
0.05 t o 10 Hz t h e ACC output is proportional t o ground velocity.
The output of t h e main feedback loop is now fed to a high pass filter
t o remove any d c offset in t h e ACC signal before further amplification. (This d c
offset is due t o drift in t h e stiffness of t h e suspension spring supporting t h e mass
and is caused mainly by temperature variations in t h e seismic vault.) This filter
is a simple high pass stage with a corner at 0.05 Hz; combined with t h e corner at
0.05 Hz of t h e main feedback loop t h e resulting output at this stage is equivalent
t o t h e output from a LP (open loop seismometer) with a natural frequency of
0.05 Hz (20 S period), a damping factor of 1 and a velocity (magnetlcoil)
transducer. The output a t this stage is referred t o as t h e VEL output.
The VEL output is the principal output of t h e Mk IIIC system. To
allow t h e signals t o be recorded on digital recorders at 10 samples/s (giving a
Nyquist of 5 Hz) the VEL sigial is passed through anti-aliasing filters to give t h e
VBB output; these a r e low pass filters cutting off at about 4 Hz and a r e described
in detail later.
To obtain t h e LPNB output the VEL output is passed through a further
series of filters and amplifiers; these filters and amplifiers a r e described in
section 3.3.
The response of t h e circuit of t h e system is now considered in detail
in three parts: t h e force feedback loop circuit, t h e overall signal response when
t h e loop is closed, and t h e filters following t h e loop. The method t h a t is used is
to derive t h e "transfer functions" of t h e various' stages from which t h e poles and
zeros can be obtained and then t o operate with these together with t h e
corresponding multipliers.
The transfer function of a system o r part of a system relates t h e
output signal to its input. I t is usually a function of t h e complex signal
frequendy s but t h e input and output need not be t h e s a m e physical quantities
although it is assumed t h a t t h e input has t h e form ~ e - ' ~in. general, a n y transfer
function of
a linear system c a n be written in t h e form
~ ( a ,+ a, S + a, S' +. a m sm)/(b o + b, S + b2s2 + b,sn).
The roots of t h e nurne r a t o r (called &OS), together with t h e roots of t h e denominator (called poles)
and t h e constant multipliers, c a n completely specify t h e transfer function.
...
A z e r o is defined as t h e value of t h e complex frequency s which
makes t h e transfer function numerically equal to zero, while a pole is defined as
t h e value of s which makes it infinite.
3.1
Transfer function of t h e f o r c e feedback loop
A block diagram of t h e feedback circuit is shown in figure Il(a).
Simplified circuits with component values and transfer functions of t w o of t h e
units in t h e loop a r e shown as figures Il(b) and I l k ) . The transfer functions of
t h e displacement transducer and preamplifier a r e derived in appendices A and B.
As t h e bandwidth of t h e s e components is very wide they c a n be coupled ,with t h e
gain of t h e wide-band channel amplifiers and phase sensitive detector and then
represented by a transducer with a transfer function of K volts/m independent of
frequency. The transfer function of t h e elements in t h e forward path a r e
referred t o as TF and those in t h e return path as TR.
The relative amplitude and phase of t h e returning f o r c e into t h e f o r c e
balance determines t h e stability of t h e circuit when t h e feedback loop is closed
(section 2.2). We first consider t h e transfer function of t h e whole loop
TL = TFTR assuming t h a t t h e returning f o r c e is not connected to t h e balance
point. Note t h a t for these calculations t h e position around t h e loop of t h e final
circuit output VOUT is immaterial and only for convenience has t h e total loop
been split into TF and TR; t h a t is t h e voltage output signal when t h e loop is
closed will not a f f e c t t h e stability. From figure 1l(a) i t c a n be seen t h a t TF is
given by MO1 (S' + 2n W os + W )-l KC(s) and TR by D(s). C ( d and D(s) a r e given
in figures I l(b) and (c) respectively. The poles, zeros and frequency independent
multipliers of TFy TR and hence TL a r e given in table 2. For this reason a method
of estimating t h e response is now given using t h e geometry of t h e s plane t o
enable t h e e f f e c t s of adjusting circuit components t o be predicted in order t o
D
maintain stability. (A t e x t book covering pole, zero constellations and s plane
geometry is given as reference (161.1 The left-hand side of t h e s plane is given in
figure 12 showing the relative positions of the constellation of poles and zeros.
Inspection of this figure allows a straight line Bode plot t o be constructed for the
amplitude response and an estimate of the phase response t o be plotted. These
approximate responses are shown in figure 13. It is seen that the Bode response is
<lO. An estimate of the amplitude of TL over this region can
flat from 0.28
be found by choosing a value of s in the centre of this band as, say, 1s l = 2. It is
seen from the transfer function TL that, with the exception of the two factors
(S + 0.28) and S, the roots are much larger than S, thus allowing the factors t o be
replaced by these roots. The amplitude response is thus given by the real part of
(S + 0.28) which for l S I = 2 gives 14.1.
this simplified transfer function 14.2 i1
Figure 13(a) also shows the amplitude response calculated from t h e exact
transfer function; it can be seen that in the band from about w = 0.4 to W = 7, the
response is close t o 14.1, the rough estimate.
TABLE 2
Poles and Zeros of the Transfer Functions of the Forward and
Return Paths of the Feedback Loop
Poles
1.
Zeros
Forward Path (TF)
(-0.09556, + 10.618)
(-0.09556,
10.618)
(0.0, 0.0)
(-666.7, 0.0)
(-12,024, 0.0)
Multiplying f a c t o r = 2.117
(- 14.71, 0.0)
(-119.0, 0.0)
-
2.
X
10"
Return Path (Tg)
(-7108, 0.0)
(-80.2, 0.0)
Multiplying f a c t o r = 197.5
Sum of 7 poles plus 3 zeros given above
Figure 13(b) shows t h e estimated phase response compared with t h e
response calculated from t h e exact transfer 'function. The agreement between
them is good over t h e seismic band of interest. The major disagreement occurs at
w > 100 and can be accounted for by t h e omission from t h e estimate of poles at
7000 and 12000.
The exact amplitude and phase responses a r e combined t o give a
Nyquist plot which, due t o t h e large range in amplitudes involved, is shown in
three sectional graphs as figures 14(a), (b) and (c). Figure 14 (c) shows t h a t t h e
system will be very stable a s t h e gain margin is 98% and t h e phase margin is 60'.
(Also plotted on this graph as a dashed line is t h e corresponding response for t h e
gain increased by a factor of 20.) Now t h e gain margin is seen t o be 65% but t h e
phase margin is reduced t o only 20' and t h e system will be unstable. Further
discussion on t h e open loop transfer function is postponed until t h e response that
results from closing t h e loop has been derived.
3.2
Transfer function of the closed loop system (ACC output)
With the loop closed t h e voltage signal output VOUT is related t o t h e
force at the balance point by the expression VoyT/Force = TF/(l + T F TR ) from
which the transfer function of VOUT relative t o ground acceleration i can be
= M TF/(l + TFTR) = M TF/(l + TL).
derived a s VOU+
To evaluate t h e poles and zeros t h e closed loop transfer function
requires the solution of a 7th order polynomial t o find t h e poles of t h e transfer
function and a 4th order polynomial t o find the zeros. In addition, evaluation of
t h e coefficients of t h e powers of S in these polynomials is tedious; a sensible way
t o find the coefficients and t h e roots is t o use a computer program. A series of
three programs have been used here t o set up t h e coefficients, find t h e roots and
evaluate t h e transfer function.
The main purpose of t h e first program of t h e sequence (FBD written
in BASIC) is t o form, from t h e values s f t h e circuit components, t h e coefficients
of the polynomials in S t h a t make up t h e closed-loop transfer function. The
program FBD also allows t h e poles and zeros of TL t o be evaluated (table 2);
these a r e required t o determine if t h e feedback system will be stable when t h e
loop is closed.
f
Given a stable system FBD gives t h e coefficients of t h e polynomial in
S and POLRT (written in FORTRAN) finds their roots (table 3). Programs ROF
and ROT (written in BASIC) can then be used t o evaluate t h e transfer function as
a function of frequency and period respectively. As well as t h e usual amplitude
and phase (4) response, phase correction (4(w)/o in seconds) and group delay
(d+b)/dw in seconds) as a function of frequency a r e also given. The amplitude
response is plotted in figure 15(a).
TABLE 3
Poles and Zeros of the Closed Loop Acceleration Responee
(ACC Output)
Poles
Total 7 poles 4 zeros
Multiplying constant to give output in v/m/s2
is 2.752 X 10''
The amplitude response expresses voltage output for given ground
acceleration. By adding a further zero the response in terms of ground velocity
can be computed and by adding two zeros at zero the response in terms of ground
displacement is obtained. This response t o ground velocity is shown in
figure 15(b).
At = 0, TFeQ due t o the capacitor in the feedback path around the
amplifier in the (P + I) stage., Thus, the acceleration 'sensitivity, Vout/ji * MTR.
Also at w = 0 the 'effect of the inductance of t h e coil (L) becomes zero so that
TF reduces t o GflR6 + R,) &d substituting for the component values
Vout/x +1.34 X 10 V/m/s From figure 15(a) the value at 100 S is seen t o be
1.30 X 10 V/m/s
'.
'
'.
S
I t is seen from figure 15(b) t h a t t h e response h a s a peak at T < 0.1.
The origin of this peak c a n be understood from t h e Bode amplitude plot for t h e
closed loop system (figure 16). The peak is seen to originate from t h e z e r o at
(- 80.3,O); ideally this z e r o should be at position (U, 0) w h e r e 0 << 9 3 and s o
would be cancelled out by t h e e f f e c t of t h e poles at (-68, f 63). Similarly t h e z e r o
at (-14*7,0) and t h e pole at (-18.4,O) should ideally coincide and cancel out. The
changes t h a t would be required to t h e circuit components t o minimise t h e e f f e c t s
-
of t h e zeros at (-80.3,O) and (-14.7,O) c a n be determined as follows. Rewriting
f a c t o r s of t h e form (S + pi) as Pi and (S + zi) as Zi in t h e transfer functions of TF
and TR, where Pi and Zi a r e respectively t h e pole and z e r o positions, then TF c a n
/(P6 6 1; K 1 and K2 a r e
b e written as K l Z I 2, /(P1 P2 P, Q PS) and TR as K
simple multipliers. Then t h e closed loop transfer function becomes
Thus, t h e four zeros in t h e closed loop transfer function a r e t h e t w o zeros of T
F
and t h e t w o poles of TR. The z e r o at (-80.3,O) was originally t h e pole at (-80.3,O)
and is equal t o (R7Cb I-'. The pole position could be made more negative by
decreasing C, but this would require a corresponding increase in R, t o maintain
t h e corner at 0.262 (lXil c i l ) . Such a change in R would increase t h e closed loop
sensitivity by t h e s a m e ratio and t h e position of t h e poles at (-68, k 6 3 ) would
also change. In practice, t h e small peak in t h e response due t o t h e z e r o at
(-80.3,O) is not of practical importance a s t h e peak is outside t h e seismic
passband of interest and would only be a problem if t h e system was operated at
very high gain in a n environment subject t o cultural noise. Similarly, t h e
difference in position of t h e pole and z e r o at w = 15 is also difficult t o minimise
but fortunately is not significant in operation although i t is in t h e passband of
interest.
Figure 17 shows t h e responses of six instruments. I t c a n b e seen that,
although t h e open l w p gains vary from 0.34 X 10 to 1.05 x 10, Vim, t h e output
sensitivities differ by only 3% in t h e signal passband (0 t o 10 Hz).
The variation at T < 0.1 (f > 10 Hz) is almost entirely due t o t h e
variation of this open loop gain. If this gain was reduced to 10 V/m, then t h e
attenuation will increase at higher frequencies but will c u t into t h e band of
interest; if i t is increased, then t h e response will progressively peak towards t h e
higher frequencies and with a value of 10' V/m will become unstable with a gain
'
margin of 37% (decreasing t o 0 at 1.6 x 10 Vim) and a phase margin of only 10'.
3.3
Transfer function of t h e signal circuits following t h e main
feedback IOOD .
(The references to circuit stages a r e f o r diagrams in P a r t 2, AWRE
Report 025183.)
T o obtain t h e VEL output, t h e output of t h e feedback loop is fed
through a combined highpass filter and amplifier s t a g e (IC9 in figure 8 of
P a r t 2). The resulting VEL signal is fed as t h e common input t o both t h e VBB a n d
LPNB filters which a r e shown in figure 10 of P a r t 2. T h e VBB filter consists of
t w o lowpass stages (IC1 and IC3) followed by a n a m i l i f i e r s t a g e IC5. T h e LPNB
f i l t e r consists of t h r e e lowpass stages (IC2, 4, 61, one highpass s t a g e (IC8) a n d a n
amplifier s t a g e (IC9). The transfer functions of t h e common ACC to VEL filter,
VBB and LPNB filters a r e given in t a b l e 4 (a), (b) and (c) respectively together
with t h e poles, zeros and multiplier factors.
The transfer function f o r t h e final outputs (VBB and LPNB) must
include those for t h e closed loop seismometer (given in t a b l e 3) plus those in
table 4(a) plus 4(b) or 4(c). The sum of these poles and zeros will give t h e outputs
in t e r m s of V/m/s2. I t is more conventional t o use t h e output of t h e VBB t r a c e in
t e r m s of ground velocity (V/m/s) and this is achieved by adding a single z e r o at
t h e origin (0,O).
The LPNB output is more usually used as a magnification, ie, response
t o ground displacement. Addition of a second z e r o at t h e origin (0,O) will give a n
output in t e r m s of V/m and t o convert t o t h e dimensionless magnification
requires t h e constant multiplier t o b e divided by 100. This magnification is t h e
value when t h e analogue electrical signal is replayed on to a pen recorder at a
sensitivity of 1 c m deflection per volt.
To summarise t h e t o t a l number of poles and zeros required for:-
ACC output to ground acceleration is 7 poles + 4 zeros to give v/m/s2,
VEL output to ground velocity
is 9 poles + 7 zeros to give v/m/s,
VBB output to ground velocity
is 13 poles + 7 zeros to give v/m/s,
LPNB output to ground displacement is 17 poles + 10 zeros to give V/m.
TABLE 4
Transfer Functions of the Circuits Following the Feedback Loop
Transfer Function
Stage/IC Number
Damping
Equivalent
Natural Frequency
wo(Tos)
Pole
Locations
Zero
t ions
Loca
Multiplierr
(a) ACC to VEL
s{r + (R2 + R,)/R~R,c~)
(%C* )-'){S
(%~2)-')
High Parr Filter
(1~9;figure 8 of Part 2)
-
0.314 (20
(-0.3135,O)
(0,O)
(-1000,O)
(-26640,O)
2 Poles
2 Zeros
1
+
+
8)
Total =
Multiplier = l
(b) VBB Filter
4 Hz L w Pass Filter
(ICl, figure 10 of Part 2)
4 Hz Low Pass Filter
w;/(s2
+ 2 m o s + W;)
W:/(s'
+ 2na,s +
IC3, figure 10 of Part 2)
Amplifier
(IC5, figure 10 of Part 2)
(h +
-
R~)/RS
Total =
4 Poles
10.1 old
(2.471) new
No Zeror Product of
Multiplier
for VBB
= 3.566 X 106 old
= (8.724 X 10')
ne!
I
TABLE 4 (Continued)
Transfer Function
Stage/IC lumber
Equivalent
Damping
n
Equivalent
Frequency
@o(T,s)
Pole
Location
Zero
Location
Multiplier
(c) LPNB Filter
llIC2
(figure 10 of Part 2)
W
W
+ 2m0s +
2/IC4
(figure 10 of Part 2)
w;/(s2
3/IC6
(E igure 10 of Part 2)*
oE/(s2 + 2nuoa + W;)
41IC8
(figure 10 of Part 2)
s/{s + (C26(R24 + ~25))-'1
51x9
figure 10 of Part 2)
{B
W);
+ ((R33+ R 3 4 + R35)/(R33+ ~ 3 4 ) ~ 3 5 ~ 3 5 ) }
{S + (~35~35)-l)
-
.
*Stage 3 is identical to Stage 2.
Total =
8 Poles
2 Zeros
Multiplier
3.2703 X 10-'
The response curve f o r t h e VBB output for ground velocity is shown as
figure 18(a) and t h a t for t h e LPNB output for ground displacement is shown as
figure 19(a). The curves for t h e phase, phase correction and group delay for each
response is shown as figures 18(b), (c) and (d), and 19(b), (c) and (d).
4.
DYNAMIC RANGE O F THE SEISMOMETER AND RECORDING
SYSTEM
The range of amplitudes of seismic signals and noise is very large; for
example, t h e rms amplitude of t h e noise in t h e pass band 0.025 to 5 Hz at a quiet
site (Queens Creek, Arizona) is about 20 nm (171, whereas t h e peak signal
amplitude recorded in this band at 30' from a magnitude 8 earthquake is
3 X lob nm. So t h a t t o record both signals with amplitude close to t h e noise level
and those from magnitude 8 earthquakes requires a recording system with a
dynamic range of over 80 db. Only digital recording systems have such large
dynamic ranges, t h e dynamic range of analogue recorders being only about 50 db.
If t h e purpose of a recording system is simply to produce a
seismogram of all signals without clippping, then i t is enough to record t h e
seismometer output at several magnifications (gains); t h e small amplitude signals
will then be available on t h e high-gain channel and t h e large amplitude signals on
t h e low gain channel. However, if small signals a r e to b e detected in t h e
presence of large signals, as is required by t h e system described here, then such a
gain ranging system is useless and t h e data have to be recorded on a single
channel of high dynamic range.
Even when a recorder with a t r u e dynamic range of 80 db is used to
record t h e output of a seismometer t h e full dynamic range of t h e system in
seismological terms is not necessarily 80 db. The principal reason for this is
-
-
t h a t the spectra of t h e system noise, seismic noise and seismic signals usually
have different shapes and dynamic range can be defined in different ways
depending on t h e assumptions made about t h e spectrum of t h e smallest and
largest signal t h e system has to record.
In this section various definitions of dynamic range are considered
and i t is shown t h a t there a r e several ways t h a t dynamic range c a n be specified.
Those quantities t h a t seem to b e t h e most useful for t h e seismograph system
described in this report a r e then derived.
There are w v e r a l dictionary definitions of dynamic range, for
example:(a) For radio: "The range of intensities in a sample of radio
as measured on a m e t e r expressed i n decibelsqB(18).
programme
...
...
(b) For television: "The ratio of maximum t o minimum brightness in
t h e original o r reproduced imageBt(18).
(c) "Of a transmission system, t h e difference in decibels between
t h e noise level of t h e system and its overload levelv (19).
Definitions (a) and (b) use measurements of t h e signal, whereas (c) specifically
admits and includes t h e system noise. None of t h e definitions specifically
includes t h e frequency band t o b e used o r t h e sensitivity level, although both a r e
implied. Based on (c) a further more specific definition could be: t h e further gain
required in 6rder t o make t h e noise level of t h e system just overload its output.
However, this also does not t a k e into account t h e spectral content of t h e
required signal. It is suggested therefore t h a t elements of (a) and (c) should be
combined t o give a definition of dynamic range f o r a seismometer system as: t h e
r a t i o of t h e largest seismic signal t h a t c a n b e recorded without -overloading t o
t h e smallest seismic signal which has its power spectral density. not less than t h a t
of the system noise at any frequency in a specified frequency band using a
specified response and sensitivity.
-
Ideally t h e dynamic range would be expressed in t e r m s of seismic
magnitude t h e scale used by seismologists t o measure t h e s i z e of seismic
sources. The definition of magnitude varies somewhat depending on epicentral
distance and wave t y p e but all magnitude formulae have t h e general form
-
where A is t h e amplitude of ground motion in microns, T t h e period and B(& h) a
t e r m t h a t corrects for t h e decay of amplitude with distance ( A ) and for depth of
focus (h). The dynamic range of a seismometer system in t e r m s of some
particular magnitude scale could thus b e specified as covering t h e range Mmin t o
Mm,, for sources at epicentral distance A', where Mmax is computed f r o m t h e
largest seismic signal t h a t can be recorded by t h e system and Mmin t h e smallest
seismic signal where largest and smallest a r e as defined in t h e previous
paragraph.
To apply t h e definition of dynamic range described above requires
t h a t not only must t h e spectrum of t h e largest (just not overloading) seismic
signal be known but also t h a t of t h e smallest. The spectrum for t h e system noise
must also be known. Whereas for an open loop seismometer this spectrum c a n be
obtained by recording t h e output of t h e system at high gain with t h e seismometer
mass "blockedM(to eliminate t h e earth motion signal), for a feedback system this
is not possible as t h e system would then revert t o an open loop system with very
high gain. If t h e noise due t o environmental e f f e c t s and t h e mechanical stability
of t h e masslspring system is ignored, t h e system noise can be estimated by
calculating and summing t h e noise spectra of t h e major components of t h e
electronic circuits and of t h e Brownian motion of t h e suspended mass, t h e latter
noise source being t h e fundamental limit t o t h e detection of ground motion.
With a properly designed system t h e maximum output will only be
limited by t h e maximum excursions at t h e output stage and this will be directly
related t o t h e voltage V of t h e power rails. If A(f) is a power spectrum for ground
z R(f) is t h e responsivity of t h e system t h a t is t h e
acceleration in (m/s 2 ) 2 / ~ and
factor in ~ / ( m / s ' ) t h a t converts from ground acceleration t o volts at frequency
f, then
(f)~(f)Gf gives t h e voltage power output over a small frequency
band 8.The total voltage power output in the pass band V,' between f i and f2,
t h e band of interest, is given by
The rms amplitude is then Vo. For a signal t h a t has a random phase
-
- t h a t is t h e
signal can be treated as noise then the maximum peak t o peak signal assuming a
Caussian distribution of amplitude will only exceed the rms amplitude 1% of t h e
time. Thus, if t h e output-stage power rails a r e f V volts, then if clipping is not
t o occur, 3V0 must be slightly less than V.
Similarly if B(f) is the power density of t h e smallest seismic signal
that can be recorded (where smallest is as defined earlier), then t h e signal
voltage power at the output is
so that t h e ratio of t h e powers of t h e largest t o smallest signal is ~ : / 9 ~ fand t h e
r a t i o of these amplitudes is Vo/3VL = V/VL. From t h e above discussion i t can be
seen t h a t t h e dynamic range is proportional to t h e output stage power rail
voltages and inversely proportional to the responsivity (or "gainw) of t h e system.
The dynamic range of a seismometer system c a n b e increased by
reducing t h e bandwidth. At t h e upper end of t h e range t h e smaller (f2 f l ) , t h e
-
larger A(f) can b e before t h e signal clips. At t h e lower end of t h e range t h e
smallest signad that can be recorded in a given bandwidth is t h a t for which at
some frequency t h e signal-to-systemnoise ratio is unity (but is nowhere less than
unity). If now the bandwidth is reduced, this may c u t out t h e frequency where t h e
signal-to-system.rroise is unity, thus enabling t h e bottom of t h e dynamic range to
be lowered t o the level set by t h e size of signal t h a t has a signal-to-system-noise
ratio of unity at some frequency in t h e new band.
4.1
4.1.1
.
System noise
Brownian noise
The fundamental limit t o the detection of ground motion is set by t h e
Brownian motion of the mass. It is shown in appendix B t h a t for a frequency band
6f the noise equivalent acceleration for a mass M, natural frequency fo, and
damping factor n is (8nkTfon 6f)IM where k is Boltzmants constant
(1.38 X 10 2' 31'~) and T is t h e absolute temperature. (Using t h e values of M, f0
and n for t h e Mk IIIC gives a noise equivalent acceleration in power of
2.66 X 10
(m/s 2, 2 / ~ ~ . )
"
4.1.2
Transducer noise
The capacitance transducer within the seismometer is a source of
noise. To determine t h e contribution from the transducer consider figure 20
which shows the circuit both in its actual form and as a simplified equivalent
circuit. The series noise equivalent resistance Rn of t h e circuit is given by
where t h e symbols a r e as defined in t h e caption t o figure 20. Using t h e numerical
value for t h e circuit elements (see figure 20) then at its operating frequency
( - 5 0 k ~ z )R, is about 4 k Q. The noise equivalent acceleration (in power) is
shown in appendix C to be 4RnkTGf {(S + 2m
+ o',)/rI2 where r is t h e
sensitivity of t h e displacement transducer in V/m. A t Long periods this becomes
($/r)' 4 ~ ~ k T 6 With
f . r = 5 X 10' Vim, w = 10.68 rad/s then at long periods t h e
(m/s 2, 2 / ~ . Above t h e
noise (power) equivalent acceleration is 3.37 X 10'
natural frequency t h e noise increases as w4 (40 db/dccade).
4.1.3
Filter noise
Consider now t h e instrument noise in t h e LPNB system. T h e system
has a bandwidth of only 0.04 Hz (40 t o 15 s period) s o t h a t using t h e value for t h e
transducer noise given above (and neglecting t h e Brownian noise which is a n
order of magnitude smaller) t h e t o t a l noise power o u t of t h e seismometer is
'.
1.4 X 10- "(m/s2) At a sensitivity of 1.3 X 104 Vlmls this gives 5 X 10.' V
rms at t h e ACC output. Assuming t h a t t h e maximum signal (with a spectrum t h e
s a m e shape as t h a t of t h e transducer noise in t h e band 40 t o 15 s period) could be
8.5 V rms, t h e amplitude range is 1.7 x 107. To digitise t h e signal at this point
and t a k e full advantage of t h e dynamic range requires t h e number of bits t o be
> m where m is given by 2m = 1 . 7 ~lo7, t h a t is 24. A digitiser with 24 bit
resolution is not readily available. It will be shown t h a t t h e system noise
approaches t h a t of t h e seismic noise in t h e LP band. For t h e purpose of
detecting signals in t h e seismic noise it is necessary t o amplify t h e signals in
order t o record them at this level (and t o include t h e system noise) with t h e
16 bits of resolution t h a t a r e available.
At t h e output of t h e feedback loop (ACC output) t h e r e will usually be
a dc offset due t o drift of t h e mass from i t s zero position which prevents simple
amplification. To remove this offset t h e signal is passed through a simple R C
low-pass filter. The corner of t h e filter is chosen t o b e at 0.05 Hz (20 S period) so
t h a t combined with t h e corner due t o t h e response of t h e loop t h e output
simulates t h a t of a conventional open loop seismometer with a natural frequency
of 0.05 Hz (20 s period) and damping factor of unity.
,
Unfortunately t h e low pass filter contributes some electronic noise.
There a r e t h r e e major contributors to t h e noise: t w o of these, amplifier current
noise and amplifier voltage noise, a r e specified (as a function of frequency) by
t h e manufacturer as current noise-density/Hz and voltage n o i s e - d e n s i t y / ~ z
respectively. The third source of noise is t h e Johnson noise of t h e source
resistance R and is given in V*/HZ by 4kTR where R is in ohms.
The most important source of noise in t h e low-pass filter arises from
t h e amplifier current-noise; this gives rise t o a voltage noise which is t h e product
of t h e impedance connected across t h e input and t h e amplifier current noise. As
t h e impedance at t h e input of t h e long period filters (due t o t h e large values of
capacitance and resistance t h a t a r e required in order to obtain a long t i m e
constant) is large so t h e voltage noise is large. The t o t a l noise of t h e low-pass
filters is obtained by summing t h e noise powers from t h e t h r e e noise sources and
this c a n b e equated to equivalent ground acceleration given t h e sensitivity (in
V/m/s2 ) a s a function of frequency at t h e acceleration output.
The power densities of t h e seismometer noise (Brownian noise and
transducer noise) and t h a t of t h e low pass filters a r e shown in figure 21. From
this figure i t can b e seen t h a t t h e filter noise exceeds t h e seismometer noise only
at frequencies of less than 0.025 Hz (periods greater than 40 S). For comparison
typical spectra of instrument noise from high quality open-loop SP and LP
seismometers a r e plotted. Also shown a r e t h e ground acceleration power
densities for Queen Creek, Arizona recognised t o be a very quiet s i t e (17) and t h e
smoothed spectra for t h e UKNET s i t e LLW when t h e noise level is high
( ~ e c e r n b e r and
) when it is low (May).
From figure 21 it can be seen that:The t o t a l instrument noise of t h e feedback instrument is
marginally b e t t e r than t h e long period open loop seismometer at all
signal frequencies less than 5 Hz (at which frequency t h e open loop
SP seismometer has a higher detectivity).
(a)
(b) The power density curve f o r t h e open loop SP seismometer
shows that, for signal periods greater than 9 S, t h e seismic noise at
t h e UKNET sites will be exceeded by t h e seismometer-electronic
noise during t h e summer months.
(c) The feedback system can just d e t e c t t h e Queen Creek noise
over t h e whole bandwidth 0.01 to 10 Hz (period 0.1 t o 100 S).
(d) The spectra of t h e seismic noise at UKNET sites during t h e
summer a r e close to those of Queen Creek for signal frequencies
between 0.05 and 0.16 Hz (6 t o 20 s period) and between 2 and 4 Hz
(0.25 to 0.5 s period).
(e) The spectra of t h e UKNET sites a r e high compared to Queen
Creek at t h e conventional short period .centre frequency of 1 Hz.
Note t h a t t h e system noise level could be reduced by increasing t h e
capacitance of t h e transducer. If t h e plate spacing were halved, t h e value of Rn
would decrease from 4 to 2.25 k Q and t h e value of t h e sensitivity r would
increase by 2. This would result in a sevkn-fold reduction in t h e transducer noise
t o 4.8 X 1 0 - ~ (m/s *l2 which is of t h e same order as t h e Brownian noise. For
LPNB t h e noise from t h e low-pass filter would b e dominant but its e f f e c t could
b e reduced by increasing t h e sensitivity of t h e closed-loop seismometer before
t h e input t o t h e filter.
4.2
Dynamic range of t h e VBB system
The combined seismometer and system noise will appear as a n
analogue signal voltage at t h e output of t h e VBB channel. 'The spectrum of this
noise, which is the product of t h e sum of t h e system noise equivalent
accelerations shown in figure 21 and the square of t h e VBB responsivity to ground
acceleration, is shown in figure 22. The total signal voltage power over t h e band
~
a maximum zero t o peak amplitude (3 rms) of
0.01 t o 4 Hz is 3.4 X 1 0 " ~giving
5.5 X 10'' V. If t h e minimum signal that can be detected is defined as being
equal t o this noise level and t h e maximum signal cannot exceed 10.5 V
(determined by t h e d c power rails), then t h e dynamic range in db is 20 log
(lO.5/(5.5 x 10-')), t h a t is 86 db. This dynamic range is only possible if t h e
detected signals have spectra t h a t have t h e same shape as t h e system noise.
The spectra of seismic signals will usually differ markedly from t h a t
of t h e system noise so t h a t an estimate of dynamic range based on system noise
is perhaps not very useful. An a t t e m p t is made to specify t h e dynamic range of
t h e VBB system in a more practical way using model spectra for signals from
earthquakes and explosions.
#
4.2.1
Using earthquake model spectra
To determine t h e magnitude mb of t h e largest earthquake t h a t can be
recorded by t h e system i t is assumed t h a t the earthquake will have a spectrum
with t h e form of t h e observed M = 7 earthquake of Berkhemer (20).
This spectrum has been converted using t h e .response of t h e VBB
channel t o give voltage power density and is shown in figure 22. The total power
output from this spectrum gives 25 V: ie, 5 V rms. Treating this signal as noise
would give 15 V zero to peak which when convolved with t h e velocity sensitivity
of t h e system of 8.5 x 10' V/m/s (figure 18(a)) results in a ground velocity of
1.76 x 10-S m/s. Dividing by 271 converts this ground velocity to t h e parameter
A/T required for t h e calculation of t h e unified magnitude mb (mb is t h e sum of
log A/T and a distance correction term). Assuming a distance correction t e r m of
3.9 this magnitude is calculated as mb = 7.3. However, this event would have
overloaded our system because we a r e limited t o a maximum z e r o to, peak
voltage signal of 10.5 V. Therefore we can scale t h e above example (M = 7,
mb = 7.3) by t h e ratio log 10.5115 t o g i v e mb = 7.1 as t h e magnitude of t h e
earthquake signal which would just not overload our system. Berkhemer also
gives theoretical spectra for earthquakes for a range of magnitudes M. That for
M = 4 has been converted t o voltage power density and is shown in figure 22.
Using t h e numerical procedure outlined above results in a unified magnitude mb
of 5.1. The curves for M = 7 and M = 4 (mb = 7.3 and mb = 5.1) can be
extrapolated to the point where the spectrum first touches t h a t of t h e system
noise. This is shown in figure 22 and calculations on this spectrum give mb = 4.4.
Thus, the magnitude range for earthquakes is mb = 4.4 t o 7.1 or 54 db.
The above discussion neglects t h e e f f e c t s of seismic noise. If t h e
minimum signal has t o have a spectrum t h a t is everywhere greater than or equal
t o some specified seismic noise spectrum, then t h e minimum magnitudes must
b e greater than that obtained using t h e system noise. The VBB output voltage
density spectra for t h e three conditions of seismic noise (Queen Creek, UKNET
in May, UKNET in December) a r e shown in figure 23. The minimum magnitudes
were found by fitting signal spectra t o t h e seismic noise spectra in such a way
t h a t t h e signal spectrum is always greater than or equal t o t h e noise spectrum,
t h e signal spectra being obtained by interpolation from t h e graphs of
Berkhemer (20) and figure 22. Calculations for these spectra would give
magnitudes of mb = 5.7 for Queen Creek, mb = 6.1 for UKNET (May) and
mb = 6.8 for UKNET (December). Note t h a t for the case of t h e seismic noise
spectrum with t h e largest amplitude UKNET (December) t h e noise is so large
that i t increases significantly t h e amplitude of signals with mb as h r g e as 7.1
and so the clipping level is set by t h e signai + noise amplitude. This means t h a t
t h e largest signal that can be recorded without clipping in t h e presence of
UKNET ( ~ e c e m b e r )noise is less than 7.1 and is in f a c t about mb = 6.9. For t h e
-
-
other two samples of seismic noise the effect of noise on t h e clipping level is
negligible. Thus, t h e range of earthquake signal magnitudes in t h e presence of
seismic noise is:Queen Creek noise
m,, =
URNET (May)
%
UKNET (December)
m,,
5.7 to 7.1
28 db
6.1 to 7.1
= 6.8 to 6.9
20 db
2 db
Using explosion model spectra
To estimate t h e dynamic range of t h e VBB system for explosion
signals it has been assumed that t h e power density spectrum of t h e explosion is
flat for ground displacement over t h e range 0.33 t o 2 NZ (0.5 t o 3.0 s period).
The voltage power density spectra a r e shown in figure 22 for t h e limiting
(clipping) case and for t h e case where the signal at 3 s period reaches t h e system
noise level. Using similar methods t o those used for t h e earthquake spectra t h e
magnitudes of t h e limiting explosion and the threshold explosion a r e calculated
a s mb = 7.2 and m,, = 3.3, a range of 78 db. In the presence of t h e three different
noise spectra the ranges become:Queens Creek:
UKNET (May):
UKNET (~ecember):
6.0 to 7.2
6.6 to 7.2
7.1 to 7.0
24 db
1 2 db
Zero
Note that because t h e maximum power (60%) of t h e assumed
explosion spectrum lies in t h e 1 t o 2 Hz band t h e magnitude of t h e signals
recorded on the VBB should only be about 0.1 magnitude units above conventional
SP systems.
Surface waves from both earthquakes and explosions
T o compute t h e clipping level for surface waves on t h e VBB system i t
is assumed t h a t t h e waves are well dispersed and t h a t t h e maximum amplitude
will b e at a single period (T = 15 S) and t h a t this will give a 0-peak output of
10.5 V. Dividing 10.5 V by t h e sensitivity of t h e system at T = 15 S (ie,
2.7 X 10' Vlm) gives t h e z e r o t o ground displacement of 3.9 X 10-S m
(3.9 X 10' nm). Assuming a distance f a c t o r B(A) of 2.0 (when t h e amplitude is
expressed in nm) and a path correction of -0.2 gives a maximum surface wave
magnitude MS of 6.4 t h a t c a n b e recorded without clipping. The magnitudes of
t h e minimum signals and t h e dynamic ranges for various noise conditions a r e
calculated and given in t a b l e X
The event magnitude ranges a r e displayed as a bar, c h a r t in figure 24.
Dynamic range of t h e LPNB system
4.3
For surface waves recorded on t h e LPNB system t h e largest
amplitude will have periods of about 20 S. If t h e maximum signal gives a 0-peak
output of 10.5 V, then as t h e sensitivity (Vim) of t h e system is 1.6 X 106 at 20 S
period (figure 19(a)) t h e maximum z e r o t o peak ground displacement is
6.6
X
10' nm which gives a n MS of 5.8. The minimum detectable signals and
dynamic ranges assuming a maximum signal of MS = 5.8 for t h e system noise and
for t h r e e different seismic noise conditions a r e given in t a b l e 6 and shown as
figure 26.
4.4
The optimum broad band response
It is obvious from t h e foregoing discussion t h a t t h e range of size of
seismic signals t h a t can b e recorded depends on t h e response of t h e system. As
t h e system is designed t o record broad band it is natural t o ask if t h e r e is any
alternative response t h a t would make b e t t e r use of t h e available dynamic range
of t h e digital recorders.
TABLE 5
Surface Wave Magnitudes Using the VBB Response
Voltage Power Density
Noise Type
0.25
- 100 S
3
System
3.4
X
10-~
5.5
Queen Creek
2.3
X
1dS
1.5
X
10-~
3
1
UKNET (nay)
URNET (~ecember)
20 log
RMS Volts
X
10.5
m
10-'
86
X
10-'
37
X
10-'
31
4.3
2.1
MS
M N
-
6.4
db
20
Dynamic Range,
db
8
*For UKHIIST (~ecember) the large amplitude of the noise reduces the magnitude of the clipping signal by 0.2
magnitude units. For all other noise conditions the clipping level remains at that calculated in the text
as MS = 6.4.
TABLE 6
Dynamic Range of LPNB Channel for Surface Waves for Various Noiae Conditions
Noise Power,
Noise Type
v2
RHS X 3,
V
Dynamic Range*
(20 log(tllls volt*
10.5
X
3 ))
db
System Noise
3.8
X
Queen Creek Noise
3.0
X
U K W T (May)
1.1
UKNET (~ecember)
'
1.2
X
-
-
10-~
5.8
X
10'-S
65
2. 5
lo-'
lo-'
1.6
X
10-~
56
3.0
3.1
X
10-~
51
3.2
10-S
1.0
X
10-
40
3.8
.
Sensitivity inV/m
Distance factor B(A)
Maximum magnitude MS
*See figure 26
Equivalent
Magnitude when
B(A)
2.0 (A )'37
1 . 6 ~10' at T t 20 s
-
= 2.0
5.8
Because t h e spectrum of seismic signals is s o variable and t h e general
features only poorly known, i t is probably best t o discuss t h e optimum response
solely in t e r m s of how best t o accommodate t h e seismic noise spectrum t o make
best use of t h e dynamic range. Assuming t h a t t h e choice of optimum amplitude
response is limited t o simple shapes high, low or band pass filtering without a n y
band s t o p filtering then t h e choice is restricted t o responses t h a t are f l a t t o
either constant ground displacement, velocity or acceleration. What is required is
a response t h a t will present to t h e digitiser a signal with all frequencies of
-
-
seismic noise in t h e pass band at about t h e s a m e amplitude. For t h e samples of
noise considered here i t c a n be seen (figures 21 and 23) t h a t a response t h a t is
f l a t for constant ground velocity does indeed best f l a t t e n t h e seismic noise
spectrum, by equalising t h e power densities at t h e ends of t h e band.
5.
COMPARISON BETWEEN RECORDINGS FROM UKNET USING
THE MK IIIC SYSTEM AND THOSE FROM BNA USING
CONVENTIONAL SEISMOMETERS
The mechanical and electronic systems used on t h e Mk IIIC a r e more
complex than those of conventional seismographs but despite this t h e system has
proved t o b e remarkably reliable. During t h e whole of t h e development a n d
operational period only one electronic component has failed (on a single
instrument) even though only commercial quality components were used.
Since t h e Mk IIIC seismometer system wag f k s t installed for continuous operation as part of UKNET, a large number of signals have been
detected. On t h e primary VBB recordings t h e signal-to-noise r a t i o for many of
t h e signals is poor but t h e conventional S P and L P seismograms which show
larger signal-to-noise ratios than those of t h e VBB c a n easily b e obtained. T h e
S P seismograms for example can be obtained by multiplying t h e spectrum of a
section of VBB record by bfw)/ab) and transforming back into t h e t i m e domain;
a(w) is t h e response of t h e VBB instrument as a function of frequency o and b(w)
is t h e response of t h e S P instrument. To obtain t h e seismogram as it would have
been recorded by other instruments b(w) is simply replaced by t h e desired
response.
5. l
Signals from an underground explosion
Figures 27 and 28 show t h e VBB P signals from an underground
explosion in E Kazakh USSR as recorded at four of t h e UKNET sites and at t h e
four BNA sites. Figures 29, 30, and 31,32 show respectively t h e S P P signals and
LP surface wave signals derived from t h e VBB. The VBB seismogram for o n e
station of UKNET, CWF, is shown for comparison. Note t h a t o n t h e VBB
seismogram t h e surface waves a r e completely masked by microseismic noise. A t
t h e t i m e of this recording t h e only station with an LPNB output available for
direct recording was WOL. I t is shown in figure 32 for comparison with t h a t
derived from t h e VBB.
A comparison of t h e magnitudes of t h e P signals as recorded on t h e
VBB and S P seismograms at e a c h station of UKNET with those obtained from t h e
four elements BNA a r r a y (equipped with open loop Geotech S-l l seismometers) is
given in table 7. Table 8 shows t h e surface wave magnitude recorded at t h e four
UKNET sites compared t o those for t h e BNA.
TABLE 7
Measurements of Body Wave Amplitudes from a
Teleseismic Underground Explosion
Station
SCK
CWF
LLW
LAM
WOL
BKN
Average mb for UKNET
Average mb for BNA
Average mb for all sites
log A/T
from VBB
log A/T
from SP
Not Measured*
2.54
2.76
2.77
2.41
2 42
2.70
2.72
6.59 f 0.08
6.67
0.07
6.64 f 0.05
*
6.46 i 0.09
6.61 f 0.06
6.54 f 0.05
*Signal-to-noise too low to give reliable readings.
All magnitudes computed on the assumption that the
distances term is 3.9.
TABLE 8
~ e ~ e s e i s m iUnderground
c
Explosion
Station
L-c
10gl~A
Period
Ts
CWF
! scK
LAM
LLW
.
H
W
W
22
m
2-
3
WOL
HD
Bw
BKN
Average MS for UKNET
Average MS for BNA
Average MS over all sites
4
*
4.31
0.07
4.52 f 0.03
0.05
4.42
*
Direct recording LP at WOL gives MS = 4.51
Uncertainties are standard errors of mean
M~ = log A + B(A) + P(T)
where B(A) = 1.68 (for A = )'74
P(T)
-0.15 for T = 15 s
= -0.18
for T = 18 s
From an inspection of the seismograms it is clear that with the
exception of station SCK signal-to-noise ratio of both the SP recordings of the P
wave and the LPNB recordings of t h e surface waves are superior at the UKNET
-
sites. A t SCK the predorninent noise appears to be at a signal period of 1.5 S
which degrades the SP trace although the LPNB recording (figure 31) appears to
be similar to those from the other UKNET sites. The amplitudes (magnitudes) of
t h e recorded signals are seen to be consistent, varying by only 0.2 magnitude
units between the mean and individual stations.
5.2
Spectra of seismic noise
The spectrum of t h e seismic noise using VBB recordings has been
investigated in t h e past (21,221, but these studies related only to local sites
around Blacknest, and did not extend beyond 20 s period into t h e LP band. In
order t o give some support for t h e reasoning and calculations concerning dynamic
range (section 4) a section of the recording from all eight sites was selected
covering a common 27 min (16384 data points) period that ended a few minutes
prior t o the arrival of t h e P wave of the explosion signal. The computed spectra
a r e shown in terms of ground acceleration power density in figures 33 (UKNET)
and 34 (BNA). To obtain a more continuous spectrum at t h e higher frequencies a
form of logarithmic smoothing has been applied -*this retains t h e narrow
bandwidth of 0.00244 S at signal periods between 100 and 26 s yet progressively
widens the bandwidth t o 0.085 s for frequencies between 4.3 and 5 Hz. The level
of the back4round 6 S microseismic noise was found t o be high. In order t o obtain
a n estimate of the seismic noise during t h e quieter summer months a section of
VBB recording was selected for a period during May when the 6 S noise was
observed t o be low. The corresponding spectra for ground acceleration for the
four UKNET sites and four BNA sites a r e shown in figures 35 and 36 respectively.
From figures 33 and 35 t h e spectra for the UKNET site LLW was chosen for
section 4 for the calculation on dynamic range.
From these spectra t h e following points of interest can be noted:(1) At short periods t h e site of SCK (North Norfolk) is excessively
noisy with a large peak at 1.5 s period and exceeding the other
-
UKNET sites at periods between 0.4 and 3 S, although i t s LP noise is
average. This explains the reason for the poor signal-to-noise ratio of
the body wave signals for SCK in figures 27 and 29. Work is now in
progress t o replace this site and a preliminary noise survey has been
undertaken (23) which indicates that t h e predominant 1.5 S noise is
common to North Norfolk and that a relatively quiet site in East
Anglia can only be found if located some tens of miles further south
of the present site.
(2)
At all sites the peak of the noise is at 6 S period during t h e
December sample but at 4 s during the May sample.
-
(3) The local sites (BNA) exhibit a second peak of noise at 2 S
period which is absent from the UKNET sites (with the exception of
(4) The high frequency qoise (0.2 to 0.3 HZ)which is mainly due to
vehicular t r a f f i c on nearby roads, etc, is, as expected, generally
higher at t h e BNA sites. probably ~ C ~ Ut h eK b e c e m b e r sample (28
December) occurred during t h e Christmas/New Year holidays t h e
cultural noise is exceptionally low whereas t h i s noise level at t h e
BNA s i t e s during May is remarkably high. (The May sample of noise
4 a m t o correspond with t h e December
was selected t o b e at
sample.)
-
( 5 ) ~ c i rboth samples of noise the UKNET r i t k (except SCK) a r e
quieter than t h e BNA s i t e s at l S period which is t h e nominal signal
'
period used f o r t h e detection of
waves. The difference is about
a n order of magnitude in power density and equivalent t o a f a c t o r of
t h r e e in amplitude.
The small peak at a period of 13 t o 15 S is seen on a l l spectra.
This peak is also significant on t h e Queen Creek noise shown in
(6)
.
figure 21.
CONCLUSIONS
6.
From experience of operating ~k IIIC seismometers in UKNET f o r
over a year t h e following conclusions can be drawn:,
(a) The system is reliable and c a n b e used t o obtain both S P and L P
seismograms from primary VBB recordings.
(b) Analysis of recordings from teleseismic earthquakes and underground explosions and of t h e background seismic noise has shown t h a t
t h e dynamic range of t h e system is consistent with t h e design
specifications.
(c) The system'is easier t o instal, is physically smaller and costs
less t o manufacture than t h e equivalent open loop LP seismometer
system. (Conventional L P seismometers a r e not commercially manufactured in t h e UK.)
(d) The calibration of t h e system should occasionally be checked
with t h e feedback circuit disconnected.
(e) Although t h e LPNB signal c a n b e successfully recovered from
VBB broadband signal offline, a second separate LP.NB channel t h a t is
transmitted with t h e VBB allows continuous real t i m e c h a r t and t a p e
recordings t o b e made.
REFERENCES
P L Willmore: "The Detection of Earth Movementsw. Methods and
Techniques in Geophysics, Runcorn. Interscience Publishers Ltd (1960)
AWRE: "The Detection and Recognition of Underground Explosionsv.
A Special Report of UKAEA (1965)
A D Beech: "A New Long Period Vertical Component Seismometer".
AWRE Report 070165 (1965)
P D Marshall, R F Burch and A Douglas: "How and Why to Record
Broad Band Seismic Signalsv. Nature (15 September 1972)
P B Felgett: "Improvements in Seismometers and Other Accelerometers". Private Communication (1966)
M J Tucker: "An Electronic Feedback Seismograph. J Sci Instr, -935
167-171 (1958)
W R MacDonald: llAcceleration Transducers of t h e Force Balance
Type". In Flight Test Instrumentation, Ed M A Perry, OxfordPergamon, pp15-23 (1961)
B S Melton and D P Johnson: "Inertial Seismograph Design
Limitations in Principle and Practicew. Proc IRE, 50 (1962)
-
B Block and R D Moore: "Measurements in t h e Earth Mode Frequency
Range by an Electrostatic Sensing and Feedback Gravimeterm. J
Geophys Res, 71,4361-4375 (1966)
-
R V Jones: "The Measurement and Control of Small Displacements".
Phys Bull, 4,325-336 (1967)
B Block and R D Moore: "Tidal t o Seismic Frequency Investigations
with a Quartz Accelerometer of New Geometryn. J Geophys Res, -97 5
1493-1505 (1970)
I W Buckner: "The Design of a Horizontal Component Feedback
Seismometer". PhD Thesis (Unpublished), University of Reading (1975)
M 3 Usher, I W Buckner and R F Burch: "A Miniature Wideband
Horizontal Component Feedback Seismometer". J Phys (E) Sci Instr,
l 0 1253-1260 (1977)
-9
M J Usher, R F Burch and C Guralp: "Wideband Feedback Seismometers". Phys Earth and Planet Int, l8, 38-50 (1979)
s:
High-Resolution Digitisation of a FrequencyB D ~ o ~ k i i "Direct
Modulated Carrier". J Phys E Sci Instr, l2, 1027-1028 (1979)
W A Lynch and 3 G Truxal: "Signals and Systems in Electrical
Engineering". McGraw-Hill (1962)
3 E Fix: "Ambient Earth Motion in t h e Period Range from 0.1 t o
S". Bull Seis Soc Am, 62 (1972)
2560
-
T C Collocott (Ed): 'IDictionary of Science and Technologytt. W & R
Chambers Ltd, Edinburgh
S Handel: "A Dictionary of Electronicsw
H Berkhemer: "The Concept of Wide Band Seismometrytt. Proceedings
of the XI1 Assemblee Generale d e la Commission Seismologique
Europeanne, Luxembourg (2 1-29 September 1970)
A Douglas and J B Young "The Estimation of of Seismic Body Wave
Signals in t h e Presence of Oceanic Microseismsw. AWRE Report
014/81 (1981)
R W Hurley: Private Communication
R F Burch: 'Private Communication
APPENDIX A
THE TRANSFER FUNCTION O F THE CAPACITANCE TRANSDUCER
AND PREAMPLIFIER
Al.
THE CAPACITANCE DISPLACEMENT TRANSDUCER
UPPER PLATE
This arrangement can be looked on as t h e bridge circuit shown below.
When the inner plate is exactly central at a distance d from t h e two
identical outer plates then, provided t h a t t h e two halves of t h e transformer
secondary windings a r e identical, t h e output of t h e bridge will be zero. Now t h e
capacitance between two plates separated by a distance d is proportional t o d-'
Let CO be the capacitance between each outer plate and t h e inner plate when it
is central. If the inner plate is moved a distance a towards t h e upper plate, then
its capacitance t o the upper plate C U is Codl(d X) and t o t h e lower plate CL is
Cod/(D + X). If t h e impedance of C U is ZU = l l s C U and of CL is ZL = llsCL,
then t h e output of t h e bridge VOUT is 2 V x ZL(ZL + ZU) V. Replacing t h e
impedances by t h e capacitances gives VouT = V(CU CL)/(CU + CL). Using t h e
.
-
-
.
-
expressions for C and CL in terms of X and d then VOUT = Vx/d giving t h e
U
transfer function a s V/d voltdmetre. For t h e Mk IIIC V - 15 V (- 5 Volts rms)
peak to peak, d 1 mm giving 1.5 X 10 V/m (5 x 10' V rmslm).
-
A2.
PREAMPLIFIER
The circuit diagram of figure 4 of P a r t 2 can be represented by
where C1 is t h e capacitance of t h e displacement transducer and is
- 10 pF.
transfer function c a n be shown t o b e
where
A = RlCIC2,
B
C
D
E
F
G
H
J
K
= ~ l ( C 1 + C2),
= R6C4,
= R4 + R5,
= ( ~ 4 R 6 ~+ 4R5R6C4 + ~ 4 ~ 5 ~ 4 ) / +( ~~ 45 1 ,
= R3C3,
R2 + R3,
= (~2R3C3)/(~2+ R3),
= (CGH + FDE)/G,
= (HG + CG + FD)/G.
-
Inserting component values results in:four zeros
t h r e e poles
with a multiplier constant of 1 X 10-'. A Bode plot c a n b e sketched as:-
I
The
C
.
.
I
I
SLOPE r 0
n
I
I
I
I
I
I
I
I
I
lb
1.;
itb6
7
,$
(010
I
log 0
From t h e above sketch t h e response is seen to b e f l a t from W = 574 ( - 100 Hz) t o
W = 2.2 X 10' (35 MHz) and t h e operating frequency of t h e Mk lllC carrier of
50 kHz (w 3 X 10' ) is in t h e middle of t h e passband. T o find t h e expression f o r
t h e gain at 50 kHz we replace S by j w in t h e transfer function and e x t r a c t t h e
real part. This gives a precise value of 22.02. However, i t will b e found t h a t t h e
r e a l part can b e simplified t o b e equal t o
-
Thus, t h e gain of t h e preamplifier is determined by t h e ratio of t h e transd-ucer
capacitance t o t h e preamplifier feedback capacitor and is multiplied by a gain
factor determined by R2 and R3.
APPENDIX B
BROWNIAN MOTION AND SEISMOMETERS
Consider a mass on a spring
1
spring stiffness = C N/m deflection.
The equipartition theorem gives t h e energy of t h e system as
+C(R) = 4kT where k = Boltzmannts constant = 1.38 X 1 0 ~ J/'' K
absolute temperature.
The mean square displacement of t h e mass ( x ) ~=
and T is
TIC.
This result implies t h a t t h e Brownian noise motion of t h e mass could
b e reduced if a very strong spring was used. This is t r u e unfortunately i t would
not b e useful a s a seismometer a s t h e inertial mass would always follow t h e
f r a m e and there would be no signal output.
-
Let us t a k e t h e case of a real seismometer with some damping and
consider its response t o a force applied t o t h e mass.
Let relative motion between mass and
f r a m e be X.
.... (B21
Equating forces MR + Bk + Cx = F,
B3 C x F
+
r=m.
However, t h e natural frequency of t h e suspension
then
W.
2
F
X + - X + U 0 X P ~ .
Q
The steady state solution for
U
0
=m~
and if we let
If w e assume t h a t t h e Brownian Force F is essentially white, then
where A is a constant and Af is t h e bandwidth
(F)'
= AM,
Thus, t h e mean square displacement = F2(response (f)) 2'/MZ
= A(response (f)) M / M ~where A is t h e power density of t h e Brownian force.
The mean square value integrated over all frequencies
= r ~ ( r e s ~ o n (f))
s e 'df /M
0
.
'.
This expression when integrated and evaluated gives
r,
Equation (BI) showed t h a t (;l2 = kT
so
Thus,
=
-
(X)'
F
=
and therefore A
-
-
woat
Q
*
boMkT f
M*Q
(response ( f j~ ~ d f .
fl
Displacement density = ( z ) ~ / H z =
h0kT
HQ
X
(response ( f ) ) 2 .
....
(B7)
Equation (84)shows t h a t t h e integral from 0 t o w o f t h e (response (f))2
is proportional to Q. The multiplying constant of equation (86) contains Q-'
therefore t h e t o t a l noise is independent of Q when accounted for over t h e whole
band of frequencies. The constant (response2) and product a r e shown in figure 37
plotted with linear co-ordinates and logarithmic co-ordinates.
We have only considered motion of t h e mass d u e t o t h e Brownian
forces acting upon it. The response of t h e system to motion of t h e case of
acceleration j; is given by
C , =wi and g
B
The steady state solution putting g
-h
Oo is
This has the 6ame form as (B3).
(f l 2
(xI2 =
((W:
- W * )+ jOowl~)2= (312 x
(response ( f ) I 2 .
-
*..m
( ~ 9 )
But (Z)2 = A- (response ( f ~ ) ~ d f ,
therefore ( y ) 2 / ~ f
A
M2
=
b0kT
, - ,
Q'
(~IS~)~XHZ.
Thus, in figure 37 t h e noise equivalent acceleration is given by sketches (1) and
(2) and sketches ( 5 ) and ( 6 ) give t h e output of t h e suspension system t o this white
input.
Now it is seen that, although we can obtain a low value of noise
equivalent acceleration by making Q large, if we include t h e natural frequency of
t h e seismometer in our bandwidth of recording, t h e t o t a l sum of t h e noise will
appear as a signal of t h e s a m e amplitude as if we had made Q small.
The seismic signal will also b e very large and concentrated about
This is undesirable and a way must b e found of removing it. If conventional
damping methods a r e used (using air damping or by connecting a resistor across a
0'
magnetfcoil transducer), then t h e system reverts t o (L)' = (4wo kT6f)IMQ and
becomes high. This is because t h e system is supplying its own power t o d a m p
itself and is doing work. If t h e s a m e e f f e c t c a n b e achieved using a n external
source, then (j;) does not increase. Provided t h a t t h e external source is
noiseless, then t h e response can be modified at will without affecting t h e signal
ratio. A feedback signal c a n be applied a s t h e source of t h e signal is now a n
external amplifier and power supply and c a n be used not only t o d a m p t h e
instrument but also t o change t h e response by causing t h e closed loop natural
frequency t o be outside t h e band of interest.
Because t h e signal-to-noise ratio is unaltered it is permissable to use
t h e open loop response characteristics when considering t h e noise equivalent
acceleration for components in t h e electronic amplifier section of t h e circuit
following t h e displacement transducer.
It can be seen from figure 21 t h a t t h e Brownian noise at 3 X 10-'l
(mfs 2 ) 2 / ~is~ one order of magnitude below t h e transducer noise. This is t h e
result of using a large mass (1.3 kg). We c a n now continue t h e discussion t o
include t h e effects of decreasing this mass and t o predict other measures t h a t
would have t o be taken in order t o retain t h e low Brownian level noise.
As shown above t h e Brownian noise equivalent acceleration
The Johnson/Nvauist noise for a resistor =
bandwidth, ie,
E 4 ~ k ~ .
(a2
-
= 4RkTB where B is t h e frequency
6f
Thus, t h e suspension system behaves like a resistor with the *olliva!ent ground
m
acceleration power density & ) 2 / ~ z= 4RskT where Rs = W.
MQ = F'
.
Thus, t h e product MQTo must b e maximised to minimise t h e noise.
L e t us now consider t h e s e parameters for t h e case where t h e only damping on t h e
system is due t o air damping. This damping f o r c e is B i (equation (82)).
B
E
"0
E
M2'
therefore Rs = B
ie, for the particular
q-
Oo i s a constant.
ma.8
For a i r damping using t h e s a m e geometry of t h e mass and capacitor plates t h e
f o r c e a a r e a of t h e mass. The weight of t h e mass = density
RS
=
area
1
ac
volume
2
X
volume, therefore
a- 1
(dimension)'
'
Therefore t h e Brownian noise power density is proportional t o
M*
'.
If we were t o miniaturise t h e seismometer t o result in a mass weight
of
150 g,
(1.3/0.15)
then
I3 = 18.
the
Brownian
noise
would
increase by
a factor of
The only method of decreasing' t h e noise is t o o p e r a t e t h e
transducer and suspension in a n evacuated vessel. This will have t h e e f f e c t of
reducing W ./Q by increasing Q while keeping W constant. (Merely changing W
is of no use a s Q is proportional t o w0.) The Mk IIIC, although enclosed in a
pressure jacket, is operated at atmospheric pressure with no= 0.01, ie, Q"5O.
For a miniature version t o operate with t h e s a m e Brownian noise level using a
mass of 150 g t h e suspension must have a Q of 50 x 18 2: 900.
APPENDIX C
THE NOISE EQUIVALENT ACCELERATION OF THE TRANSDUCER
NOISE AND BROWNIAN NOISE
A block diagram is shown in figure 38. ln' section 4.1.2 it was s t a t e d
t h a t t h e transducer noise can b e equated t o t h a t of a series resistor R, a n d thus
has a white noise power density spectrum. Whereas in appendix B w e derived t h e
Brownian noise acting on .the seismometer mass as a n equivalent acceleration
power density (= 4RskT where R, = w ,/MQ) and t h e n used t h e suspension
response t o determine t h e displacement output, for t h e transducer noise we need
t o work back through t h e suspension response t o find t h e equivalent acceleration
power density.
Thus, t h e output noise of t h e transducer of 4RnkT volts2 IHz becomes
where r is t h e transducer sensitivity in V/m.
However, t h e Brownian noise acceleration power density (y) 'IHZ = PRskT.
So t h e t o t a l noise acceleration power density is (Z)'IHZ
+ C?)'/HZ. This sum
represents t h e detection level of t h e seismometer in t e r m s of ground acceleration and assumes no other source of electrical or mechanical noise. This t o t a l
noise can then be used with t h e transfer function of t h e closed loop seismometer
t o derive t h e power density of t h e noise at t h e output of t h e system as
..
..
It is useful to note how (z)'/Hz varies with r and with w
From t h e
equation shown above (z)2 / ~ az (r '(response (f)12)- Thus, immediately we see
t h e improvement by increasing t h e sensitivity r of t h e transducer. Figure 39
shows a sketch of (2) 2 / for
~ ~constant r but with varying values of t h e
seismometer natural frequency w o. From this it c a n be seen t h a t for
frequencies >>U t h e noise equivalent is independent of w o, but for frequencies
wo t h e need t o make w a s low as possible is apparent.
Figure 1 Locations of
Broad
Band
Recording S i t e s
/-CORNER
0
DEPENDS ON
0
LOG FREQUENCY
Figure 3
Sketch of Response to Acceleration of
Sprung Mass wit h Displacement Transducer
-
OU'TPUT
tSlGNAL
vo
MAGNET /COIL
FEEDBACK
TRANSDUCER
G. NIAMPERE
GROUND
MOTION
?
f
AMPLIFIED TRANSDUCER
SENSITIVITY = A VOLTSJM
,
Figure 4 ( a ) Schematic
-
Diagram of
62
Feedback Seismometer
FORCE
VOLTS
V 0 LT S
FORCE
Figure 4 ( b ) : 4 (c )
Block
Diagrams for Feedback Seismometer
LOG FREQUENCY
Figure 6
Response to Ground Velocity of an Overd a m p e d Accelerometer
t
0
UDE
Figure 7
Example of
Root
1
'
LEAD
PHASE
LAG
Locus Plot ( Nyquist PI o t )
CURRENT PASSED
1HROUGH COlL
h
,'
SYSTEM OUTPUT
3 MINUTES (SAY )
TIME
Figure 8
Response of ~ o n v e tnional Long Period Seismometer
to a Current Step Passed through i t s Calibration Coil
( a ) OPEN LOOP SYSTEM
( b ) FEEDBACK SYSTEM WlTH TWO COILS
(C
Figure 9
1 FEEDBACK SYSTEM WlTH COMMON COlL
Calibration Coil Seismometer Combinat ions
M
-
Dl SP
TRANSD'
PR€
AMP
-
CHANNEL
AMPS
-
r
-
PHASE
SENSITIVE
DETECTOR
CONTROLLER,
-
-
ACC
OUT PUT
7
VEL
ANTI ALIAS
AND A M P
LONG PERIOD
FILTER
AND AMP
Figure 10. Block Diagram of Signal P a t h s
OUTPUT
GROUND
ACCELERATION
Y
1
FORCE
BALANCE
DISPLACEMENT
ACCELERATION
OF
VOLT S
MASS
VOLTS
OUT
1
K
- C(S)
s2+2n00s+ob
-
M
r i
NEWTONS
A
D(s)
t
8
+
v
#
TR
IS THE TRANSFER FUNCTION OF THE
MECHANICAL S PRINGIMASS SYSTEM ( m l m l s 2 )
1
S
.
2 n o s 2 0
=
=
M
K
MASS OF SElSMOMETER INERTIAL MASS = 1.3 Kg
DISPLACEMENT TRANSDUCER SENSITIVITY AFTER
GAlN FROM PREAMPLI FlER AND C H A N N E L AMPLIFIER
AND PHASE SENSITIVE DETECTOR = 0.34 X 106 v l m
Figure 11 (a) Block Diagram of Force Balance
Feed back Seismometer
C1
m
II
R5
'S
L0WPASS
FILTER
PHASE ADVANCE
CONTROLLER
PROPORTIONAL +
l INTEGRAL
CONTROLLER
Figure 11 (b) Circuit and Transfer Function of
Block C(s) of Figure11 ( a )
m, C4
FORCE
(N EWTONS)
VOLT S
R6
R6 = 1.62Mfl
R7 = 5.75Kn
L =0.8H
G = 158Nl AMP
C4 = 2 . 2 ~F
G
D(s'
=
C
G
R7
L
m
(CONTROLS CLOSED LOOP GAIN ( V O L T S l m I s 2 ) )
(RESISTANCE OF FEEDBACK TRANSDUCER COIL 1
(INDUCTANCE OF FEEDBACK TRANSDUCER COIL 1
(MOTOR CONSTANT OF FEEDBACK TRANSDUCER
(CONTROLS DAMPING OF CLOSED LOOP SEISMOMETER
(S+ ( ~ 6 ~ 1 ) " ' )
( S ~ + ( ( R ~ R ~ C ~ + L ) I R ~ C L L ) S +R~6RC L
~ L+) R ~ ) I
Figure l 1 (c) Circuit and Transfer Function of
Block D(s) of Figurell(a)
X
0.096
10.6
NOT TO SCALE
-
I
a COMPLETE CONSTELLATION
NOT TO SCALE
b
Figure 12
CONSTELLATION OVER BAND OF
INTEREST
\
'4r
-X
0.096
10.6
Constellation of Poles and Zeros for Open Circuit
Total Loop ( TL = TF X TR )
50
I
.
I
0
I
a
W
n
4
0
I
LI
V)
W
W
=0
-
0-
W
0
W
V)
a
I
Q
-
-100
-
--
ESTl MATED
) C
0
%
\
- 50-
.
0.1
I
1
I
I
10
100
1000
FREQUENCY, O
Figure 1 3 b ) Estimated and Exact
~ r a r i s f e r Function
Phase
of
the Loop
Figure l4(a) Nyquist Diagram f o r
U
Between
9.6
and 11.5
Figure l b ( b ) . Nyquist Diagram for w between 0.06 and 8 7 and
b e t w e e n 12.1 a n d 3 8
Figure 1 L ( c ) . Nyquist
Diagram
for
between 75 and 1633
1
10
PERIOD, s
Figure 15(a). Response of Closed Loop to Ground Acceleration
jo
7K
119 80.9
-x-oo---------.X-X~)
513
11.7
1 8.4
___)
0.26
U
NOT TO SCALE
Figure 16 (a ). Pole Zero Constellation for Closed Loop Velocity Response
0.26
14.7
.
NOT TO SCALE
*
LOG FREQUENCY, O
Figure 16(b) Bode Plot for Closed Loop Velocity Response
PERIOD,
S
Figure 19 (a) LPN B Response to Ground
84
Displacement
A( 2 c )
I
-
-
Vn a
"0
AMP
CS
Ce
mm
Re
--
-
CS
TRANSDUCER
CAPACITANCE
Ce
PARALLEL STRAY CAPACITANCE
Re
EFFECTIVE PARALLEL RESISTANCE
[ B I A S + STRAYS 1
*
1
-
~
2
2
0
0
~
~
~
~
NOISE EQUIVALENT RESISTANCE
OF AMPLIFIER
Rni
r
S E N S I T I V I T Y OF T R A N S D U C E R
P
Figure 20. Noise Equivalent Circuit for Displ cement Transducer
OPEN LOOP
SHORT PERIOD
UKNET (DEC 1
LIK NET ( M A Y )
OPEN LOOP
LONG PERIOD
QUEEN CREEK
ELECTRON l C
TRANSDUCER
BROWN IAN
-22
10
0.1
I
I
I
I
I
I
I
0.2
0.5
1
2
5
10
20
PERIOD, s
l
l
E0
I
l0
I
Figure 2 1. Instrument Noise and Seismic Noise Acceleration
Power Density Spectra
I
-
-
SYSTEM NOISE
PER 100,s
Figure 22.
. Spectra of V 0 B Output Signals for Model
Events and System Noise
I)
PERIOD, S
Figure23. Spectra of V B B Output
System Noise
for Seismic and
A
CONSIDERING
SYSTEM N O I S E ONLY
B
C
D
CONSIDERING SEISMIC NOISE WlTH QUEEN CREEK SPECTRUM
CONSIDERING SEISMIC NOISE WlTH
UKNET (MAY )
CONSIDERING SEISMIC NOISE WlTH
UKNET [ DECEMBER 1
Figure 24. Ranges of Magnitude for V B B Out put Signals
5
10
20
50
100
PERIOD, S
Figure 25. Spectra of L P N B Output for System and
Seismic Noise
Figure 26. Ranges of Magnitude for LPNB Output Signals
SCK
CWF
LLW
~
l
LAM
Figure 27. Velocity
Broad Band ( V B B )
U K N e t Stations.
Signals
from Four
WOL
BKN
I
l
l
Figure 28
Velocity Broad B a n d ( V B B )
Four Local Stations
I
S i g n a l s from
SCK
CWF
-v
Figure 29. Short
Period
Stations )
Signals
from V B B (Four UKNet
Figure 30. Short Period Signals
Stations )
from
VBB
( Four
Local
C W F VBB
CWF
Figure 31. Surface Waves
Stations.
Derived
from
V B B ( Four ( J K N ~ ~
l
CONVENTIONAL LP
-;*.gf i ~ , p
WOL
i
DERIVED FROM V B B
Figure 32. Surface Waves Derived
Stations .)
from
V B B (Four Local
PERIOD, s
Figure 3 3 .
Smoothed Spectra of Seismic Noise at
Fwr UKNet Sites (December)
Figure 3 4 .
Smoothed Spectra of Seismic Noise at Four BNA Sites (December)
PERIOD, S
Figure 3 5 .
Smoothed Spectra of Seismic Noise at Four UKNet Sites
(May)
PERIOD,
C
Figure 3 6 .
s
Smoothed Spectra of Seismic Noise at Four BNA Sites (May)
0 SMALL
O SMALL
0 LARGE
1
Q LARGE
LOG f
0 LARGE
f0
LOG f
0 SMALL
fo
F l GLlRE 37.
LOG f
Response to Brownian Forces for Different Values of
105
'Q'
- - - - - -1
I
l
1 TRANSOUCER EOUIVALENT
I ACCELERATION
I (ZI~IHZ
= 4Rn kT
I
1
I
I
l
1
I BROWNIAN EOUIVALENT
I ACCELERATION
I
I ( ~ 1 H~z 1 4 R s kT
I WHERE RszDolMQ
I
OPEN LOOP
SUSPENSION SYSTEM
h.Q.M
RESPONSE (1)
TRANSDUCER NOISE
MSPLACEMENT
TRANOUCER
SENSlTiVlfY
r VOLTS1 m
POWER DENSITY
= 4Rn kT VOLTS~IHZ
1
I
I
I
I
I
-l
l
CLOSED LOOP
TRANSFER
TFff)
FUNCTION
FIGURE 3 8.
(( Y ) z l H r + ( Z ) Z l H z ) r (TF ( f ) j 2
=
LkT
(
RS
+h
( Tf (f)12
(r2l~ESPOHSE1f1121)
Block Diagram t o Determine Transducer Noise Equivalent Acceleration
0.01
0.1
LOG f
FIGURE 39
1
,Hz
Variation of Transducer Noise' Equivalent
Acceleration with Natural Frequency.
overall a c c u r i t y c l a s s i f i c a t i o n of mheet
......
~
~
.......~........~........~.........P........~......... .
i n f o r u t i o b . I f i t l r neceararg t o o u t e r
clamsified information, t h e box concerned rust be marked t o i n d i c a t e t h e c ~ r i f i c a t i o n*g (R), (C) o r (S)).
(A. f a r an pomrible t h i s mheet r h w l d contain only uncl.ssiffed
,
1. DRIC Reference ( i f lurovn)
5.
O r i g i n a t o r ' s Code
( i f known)
5a. Sponsoring Agency ' S
Code ( i f known)
2.
Orfginator'r Reference
6.
4.
b e n c y Raference
-
AWRE Report No. 024/83
Report S e c u r i t y
Clumification
UNLIMITED
O r f g i r u t o r (Corporate b t h o r ) tim and outi ion
Atomic Weapons Research Establishment, Aldermaston, Berkshire
6.
Sponroring Agency (Contract Authority) U..a md l o c a t i o n
7.
3.
-
Title
The Mk IIIC Vertical Component Force Balance Seismometer System.
Part 1: Design and Development
7a. T i t l e i n Foreign Language ( i n t h e case of T r m r l a t i o n )
7b. Prerented a t ( f o r Conference Paperr). T i t l e , Place and Date of Conference
8. Author l.Surnama, I n i t i a l s
9.
9b. Authorr 3, 4
-
Burch R F
11. Contract Number
Author 2
12. Period
-
-
....
10.
.
13. P r o j e c t
Date
PP
ref
February 1984108 23
14. Other Refermcee
-
-
15. D i r t r i b u t i o n Statement
No restriction
16. Darcriptorr (or Keyvords) (TEST)
Seismometers
Abrttact
AWRE Blacknest have developed, in co-operation with the University of Reading,
a broad band seismometer system for the measurement of the vertical component
of ground motion. It cgnsists essentially of a short period seismometer to
which a capacitance displacement transducer has been added. By the use of
electronic feedback, a force balance system is operated which enables the
instrument to provide adequate signals over the frequency band of seismological
interest (typically 0.01 to 10 HZ) and eliminates the requirement for separate
short period and long period instruments.
i
1/--pages
Пожаловаться на содержимое документа